Pub Date : 2026-02-01Epub Date: 2025-10-04DOI: 10.1016/j.spa.2025.104785
M. Aleandri , P. Dai Pra
A dynamical system that undergoes a supercritical Hopf’s bifurcation is perturbed by a multiplicative Brownian motion that scales with a small parameter . The random fluctuations of the system at the critical point are studied when the dynamics starts near equilibrium, in the limit as goes to zero. Under a space–time scaling the system can be approximated by a 2-dimensional process lying on the center manifold of the Hopf’s bifurcation and a slow radial component together with a fast angular component are identified. Then the critical fluctuations are described by a “universal” stochastic differential equation whose coefficients are obtained taking the average with respect to the fast variable.
{"title":"Long time fluctuations at critical parameter of Hopf’s bifurcation","authors":"M. Aleandri , P. Dai Pra","doi":"10.1016/j.spa.2025.104785","DOIUrl":"10.1016/j.spa.2025.104785","url":null,"abstract":"<div><div>A dynamical system that undergoes a supercritical Hopf’s bifurcation is perturbed by a multiplicative Brownian motion that scales with a small parameter <span><math><mi>ɛ</mi></math></span>. The random fluctuations of the system at the critical point are studied when the dynamics starts near equilibrium, in the limit as <span><math><mi>ɛ</mi></math></span> goes to zero. Under a space–time scaling the system can be approximated by a 2-dimensional process lying on the center manifold of the Hopf’s bifurcation and a slow radial component together with a fast angular component are identified. Then the critical fluctuations are described by a “universal” stochastic differential equation whose coefficients are obtained taking the average with respect to the fast variable.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104785"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145247888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-18DOI: 10.1016/j.spa.2025.104804
Martin Larsson, Shukun Long
Markovian projections arise in problems where we aim to mimic the one-dimensional marginal laws of an Itô semimartingale by using another Itô process with Markovian dynamics. In applications, Markovian projections are useful in calibrating jump–diffusion models with both local and stochastic features, leading to the study of the inversion problems. In this paper, we invert the Markovian projections for pure jump processes, which can be used to construct calibrated local stochastic intensity (LSI) models for credit risk applications. Such models are jump process analogues of the notoriously hard to construct local stochastic volatility (LSV) models used in equity modeling.
{"title":"Inverting the Markovian projection for pure jump processes","authors":"Martin Larsson, Shukun Long","doi":"10.1016/j.spa.2025.104804","DOIUrl":"10.1016/j.spa.2025.104804","url":null,"abstract":"<div><div>Markovian projections arise in problems where we aim to mimic the one-dimensional marginal laws of an Itô semimartingale by using another Itô process with Markovian dynamics. In applications, Markovian projections are useful in calibrating jump–diffusion models with both local and stochastic features, leading to the study of the inversion problems. In this paper, we invert the Markovian projections for pure jump processes, which can be used to construct calibrated local stochastic intensity (LSI) models for credit risk applications. Such models are jump process analogues of the notoriously hard to construct local stochastic volatility (LSV) models used in equity modeling.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104804"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-07DOI: 10.1016/j.spa.2025.104828
Wen Sun
We study the condensation phenomenon for the invariant measures of the mean-field model of reversible coagulation–fragmentation processes conditioned to a supercritical density of particles. It is shown that when the parameters of the associated balance equation satisfy a subexponential tail condition, there is a single giant particle that corresponds to the missing mass in the macroscopic limit. We also show that in this case, the rest of the particles are asymptotically i.i.d according to the normalised equilibrium state of the limit hydrodynamic differential equation. Conditions for the normal fluctuations and the -stable fluctuations around the condensed mass are given. We obtain the large deviation principle for the empirical measure of the masses of the particles at equilibrium as well.
{"title":"On the Condensation and fluctuations in reversible coagulation–fragmentation models","authors":"Wen Sun","doi":"10.1016/j.spa.2025.104828","DOIUrl":"10.1016/j.spa.2025.104828","url":null,"abstract":"<div><div>We study the condensation phenomenon for the invariant measures of the mean-field model of reversible coagulation–fragmentation processes conditioned to a supercritical density of particles. It is shown that when the parameters of the associated balance equation satisfy a subexponential tail condition, there is a single giant particle that corresponds to the missing mass in the macroscopic limit. We also show that in this case, the rest of the particles are asymptotically <em>i.i.d</em> according to the normalised equilibrium state of the limit hydrodynamic differential equation. Conditions for the normal fluctuations and the <span><math><mi>α</mi></math></span>-stable fluctuations around the condensed mass are given. We obtain the large deviation principle for the empirical measure of the masses of the particles at equilibrium as well.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104828"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-12DOI: 10.1016/j.spa.2025.104831
Stein Andreas Bethuelsen , Malin Palö Forsström
Forsström et al. (2025) recently introduced a large class of -valued processes that they named Poisson representable. In addition to deriving several interesting properties for these processes, their main focus was determining which processes are contained in this class.
In this paper, we derive new characteristics for Poisson representable processes in terms of certain mixing properties. Using these, we argue that neither the upper invariant measure of the supercritical contact process on nor the plus state of the Ising model on within the phase transition regime is Poisson representable. Moreover, we show that on any non-extremal translation invariant state of the Ising model cannot be Poisson representable. Together, these results provide answers to questions raised in Forsström et al. (2025).
{"title":"Mixing for Poisson representable processes and consequences for the Ising model and the contact process","authors":"Stein Andreas Bethuelsen , Malin Palö Forsström","doi":"10.1016/j.spa.2025.104831","DOIUrl":"10.1016/j.spa.2025.104831","url":null,"abstract":"<div><div>Forsström et al. (2025) recently introduced a large class of <span><math><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow></math></span>-valued processes that they named Poisson representable. In addition to deriving several interesting properties for these processes, their main focus was determining which processes are contained in this class.</div><div>In this paper, we derive new characteristics for Poisson representable processes in terms of certain mixing properties. Using these, we argue that neither the upper invariant measure of the supercritical contact process on <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> nor the plus state of the Ising model on <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> within the phase transition regime is Poisson representable. Moreover, we show that on <span><math><mrow><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo></mrow></math></span> <span><math><mrow><mi>d</mi><mo>≥</mo><mn>2</mn><mo>,</mo></mrow></math></span> any non-extremal translation invariant state of the Ising model cannot be Poisson representable. Together, these results provide answers to questions raised in Forsström et al. (2025).</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104831"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-12DOI: 10.1016/j.spa.2025.104832
Anton Tiepner , Lukas Trottner
<div><div>We study a stochastic heat equation with piecewise constant diffusivity <span><math><mi>ϑ</mi></math></span> having a jump at a hypersurface <span><math><mi>Γ</mi></math></span> that splits the underlying space <span><math><msup><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mrow><mi>d</mi><mo>≥</mo><mn>2</mn><mo>,</mo></mrow></math></span> into two disjoint sets <span><math><mrow><msub><mrow><mi>Λ</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>∪</mo><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>.</mo></mrow></math></span> Based on multiple spatially localized measurement observations on a regular <span><math><mi>δ</mi></math></span>-grid of <span><math><msup><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow><mrow><mi>d</mi></mrow></msup></math></span>, we propose a joint M-estimator for the diffusivity values and the set <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> that is inspired by statistical image reconstruction methods. We study convergence of the domain estimator <span><math><msub><mrow><mover><mrow><mi>Λ</mi></mrow><mrow><mo>̂</mo></mrow></mover></mrow><mrow><mo>+</mo></mrow></msub></math></span> in the vanishing resolution level regime <span><math><mrow><mi>δ</mi><mo>→</mo><mn>0</mn></mrow></math></span> and with respect to the expected symmetric difference pseudometric. As a first main finding we give a characterization of the convergence rate for <span><math><msub><mrow><mover><mrow><mi>Λ</mi></mrow><mrow><mo>̂</mo></mrow></mover></mrow><mrow><mo>+</mo></mrow></msub></math></span> in terms of the complexity of <span><math><mi>Γ</mi></math></span> measured by the number of intersecting hypercubes from the regular <span><math><mi>δ</mi></math></span>-grid. Furthermore, for the special case of domains <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> that are built from hypercubes from the <span><math><mi>δ</mi></math></span>-grid, we demonstrate that perfect identification with probability tending to one is possible with a slight modification of the estimation approach. Implications of our general results are discussed under two specific structural assumptions on <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>. For a <span><math><mi>β</mi></math></span>-Hölder smooth boundary fragment <span><math><mi>Γ</mi></math></span>, the set <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> is estimated with rate <span><math><msup><mrow><mi>δ</mi></mrow><mrow><mi>β</mi></mrow></msup></math></span>. If we assume <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> to be convex, we obtain a <span><math><mi>δ</mi></math></span>-rate. While our approach only aims at optimal domain estimation rates, we also demonstrate consistency of ou
{"title":"Multivariate change estimation for a stochastic heat equation from local measurements","authors":"Anton Tiepner , Lukas Trottner","doi":"10.1016/j.spa.2025.104832","DOIUrl":"10.1016/j.spa.2025.104832","url":null,"abstract":"<div><div>We study a stochastic heat equation with piecewise constant diffusivity <span><math><mi>ϑ</mi></math></span> having a jump at a hypersurface <span><math><mi>Γ</mi></math></span> that splits the underlying space <span><math><msup><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mrow><mi>d</mi><mo>≥</mo><mn>2</mn><mo>,</mo></mrow></math></span> into two disjoint sets <span><math><mrow><msub><mrow><mi>Λ</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>∪</mo><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>.</mo></mrow></math></span> Based on multiple spatially localized measurement observations on a regular <span><math><mi>δ</mi></math></span>-grid of <span><math><msup><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow><mrow><mi>d</mi></mrow></msup></math></span>, we propose a joint M-estimator for the diffusivity values and the set <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> that is inspired by statistical image reconstruction methods. We study convergence of the domain estimator <span><math><msub><mrow><mover><mrow><mi>Λ</mi></mrow><mrow><mo>̂</mo></mrow></mover></mrow><mrow><mo>+</mo></mrow></msub></math></span> in the vanishing resolution level regime <span><math><mrow><mi>δ</mi><mo>→</mo><mn>0</mn></mrow></math></span> and with respect to the expected symmetric difference pseudometric. As a first main finding we give a characterization of the convergence rate for <span><math><msub><mrow><mover><mrow><mi>Λ</mi></mrow><mrow><mo>̂</mo></mrow></mover></mrow><mrow><mo>+</mo></mrow></msub></math></span> in terms of the complexity of <span><math><mi>Γ</mi></math></span> measured by the number of intersecting hypercubes from the regular <span><math><mi>δ</mi></math></span>-grid. Furthermore, for the special case of domains <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> that are built from hypercubes from the <span><math><mi>δ</mi></math></span>-grid, we demonstrate that perfect identification with probability tending to one is possible with a slight modification of the estimation approach. Implications of our general results are discussed under two specific structural assumptions on <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>. For a <span><math><mi>β</mi></math></span>-Hölder smooth boundary fragment <span><math><mi>Γ</mi></math></span>, the set <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> is estimated with rate <span><math><msup><mrow><mi>δ</mi></mrow><mrow><mi>β</mi></mrow></msup></math></span>. If we assume <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> to be convex, we obtain a <span><math><mi>δ</mi></math></span>-rate. While our approach only aims at optimal domain estimation rates, we also demonstrate consistency of ou","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104832"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-05DOI: 10.1016/j.spa.2025.104817
Lena Kuwata
In this work, we introduce a spatial branching process to model the growth of the mycelial network of a filamentous fungus. In this model, each filament is described by the position of its tip, the trajectory of which is solution to a stochastic differential equation with a drift term which depends on all the other trajectories. Each filament can branch either at its tip or along its length, that is to say at some past position of its tip, at some time- and space-dependent rates. It can stop growing at some rate which also depends on the positions of the other tips. We first construct the measure-valued process corresponding to this dynamics, then we study its large population limit and we characterise the limiting process as the weak solution to a system of partial differential equations.
{"title":"A generalised spatial branching process with ancestral branching to model the growth of a filamentous fungus","authors":"Lena Kuwata","doi":"10.1016/j.spa.2025.104817","DOIUrl":"10.1016/j.spa.2025.104817","url":null,"abstract":"<div><div>In this work, we introduce a spatial branching process to model the growth of the mycelial network of a filamentous fungus. In this model, each filament is described by the position of its tip, the trajectory of which is solution to a stochastic differential equation with a drift term which depends on all the other trajectories. Each filament can branch either at its tip or along its length, that is to say at some past position of its tip, at some time- and space-dependent rates. It can stop growing at some rate which also depends on the positions of the other tips. We first construct the measure-valued process corresponding to this dynamics, then we study its large population limit and we characterise the limiting process as the weak solution to a system of partial differential equations.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104817"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-13DOI: 10.1016/j.spa.2025.104779
Mathias Beiglböck , Gudmund Pammer , Lorenz Riess
Change of numeraire is a classical tool in mathematical finance. Campi–Laachir–Martini (Campi et al., 2017) established its applicability to martingale optimal transport. We note that the results of Campi et al. (2017) extend to the case of weak martingale transport. We apply this to shadow couplings (in the sense of Beiglböck and Juillet (2021)), continuous time martingale transport problems in the framework of Huesmann–Trevisan (Huesmann and Trevisan, 2019) and in particular to establish the correspondence of stretched Brownian motion with its geometric counterpart. From a mathematical finance perspective, the geometric (stretched) Brownian motion and the corresponding geometric Bass local volatility model are more natural, and via the change of numeraire transform the efficient and well-understood algorithm for the Bass local volatility model can be adapted to this geometric counterpart.
数值变换是数学金融中的一种经典工具。Campi - laachir - martini （Campi et al., 2017）建立了其对鞅最优运输的适用性。我们注意到Campi等人（2017）的结果扩展到弱鞅输运的情况。我们将其应用于阴影耦合（Beiglböck和juliet（2021）的意义上），Huesmann - Trevisan框架中的连续时间矩阵输移问题（Huesmann和Trevisan， 2019），特别是建立拉伸布朗运动与其几何对应的对应关系。从数学金融的角度来看，几何（拉伸）布朗运动和相应的几何Bass局部波动模型更自然，通过改变数值变换，Bass局部波动模型的高效且易于理解的算法可以适应于这种几何对应物。
{"title":"Change of numeraire for weak martingale transport","authors":"Mathias Beiglböck , Gudmund Pammer , Lorenz Riess","doi":"10.1016/j.spa.2025.104779","DOIUrl":"10.1016/j.spa.2025.104779","url":null,"abstract":"<div><div>Change of numeraire is a classical tool in mathematical finance. Campi–Laachir–Martini (Campi et al., 2017) established its applicability to martingale optimal transport. We note that the results of Campi et al. (2017) extend to the case of weak martingale transport. We apply this to shadow couplings (in the sense of Beiglböck and Juillet (2021)), continuous time martingale transport problems in the framework of Huesmann–Trevisan (Huesmann and Trevisan, 2019) and in particular to establish the correspondence of stretched Brownian motion with its geometric counterpart. From a mathematical finance perspective, the geometric (stretched) Brownian motion and the corresponding geometric Bass local volatility model are more natural, and via the change of numeraire transform the efficient and well-understood algorithm for the Bass local volatility model can be adapted to this geometric counterpart.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104779"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145467325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-08DOI: 10.1016/j.spa.2025.104827
Wenxuan Chen , Linjie Zhao
We study a weakly asymmetric exclusion process with long jumps and with infinitely many extended reservoirs. We prove that the stationary fluctuations of the process are governed by the generalized Ornstein–Uhlenbeck process or the stochastic Burgers equation with Dirichlet boundary conditions depending on the strength of the asymmetry of the dynamics.
{"title":"Stationary fluctuations for the WASEP with long jumps and infinitely extended reservoirs","authors":"Wenxuan Chen , Linjie Zhao","doi":"10.1016/j.spa.2025.104827","DOIUrl":"10.1016/j.spa.2025.104827","url":null,"abstract":"<div><div>We study a weakly asymmetric exclusion process with long jumps and with infinitely many extended reservoirs. We prove that the stationary fluctuations of the process are governed by the generalized Ornstein–Uhlenbeck process or the stochastic Burgers equation with Dirichlet boundary conditions depending on the strength of the asymmetry of the dynamics.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104827"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-20DOI: 10.1016/j.spa.2025.104805
Zixin Feng , Dejian Tian , Harry Zheng
The paper investigates the consumption–investment problem for an investor with Epstein–Zin utility in an incomplete market. A non-Markovian environment with unbounded parameters is considered, which is more realistic in practical financial scenarios compared to the Markovian setting. The optimal consumption and investment strategies are derived using the martingale optimal principle and quadratic backward stochastic differential equations (BSDEs) whose solutions admit some exponential moment. This integrability property plays a crucial role in establishing a key martingale argument. In addition, the paper also examines the associated dual problem and several models within the specified parameter framework.
{"title":"Consumption–investment optimization with Epstein–Zin utility in unbounded non-Markovian markets","authors":"Zixin Feng , Dejian Tian , Harry Zheng","doi":"10.1016/j.spa.2025.104805","DOIUrl":"10.1016/j.spa.2025.104805","url":null,"abstract":"<div><div>The paper investigates the consumption–investment problem for an investor with Epstein–Zin utility in an incomplete market. A non-Markovian environment with unbounded parameters is considered, which is more realistic in practical financial scenarios compared to the Markovian setting. The optimal consumption and investment strategies are derived using the martingale optimal principle and quadratic backward stochastic differential equations (BSDEs) whose solutions admit some exponential moment. This integrability property plays a crucial role in establishing a key martingale argument. In addition, the paper also examines the associated dual problem and several models within the specified parameter framework.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104805"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-10-24DOI: 10.1016/j.spa.2025.104810
Muneya Matsui , Thomas Mikosch , Olivier Wintenberger
We consider a regularly varyingstationary sequenceof random variables with tail index . For this sequence we study the joint convergenceof sums, -type moduli and maxima. We focus on ratio statistics, including the studentized sums and sums normalized by the corresponding maxima, and study the existence of moments for the limit ratios. We consider particular examples of processes whose limit ratios possess all moments as in the iid setting. But, in contrast to the latter situation, there also exist dependent sequences where certain moments of the limit ratio are infinite. This phenomenon results from extremal clusters in the sequence.
{"title":"Moments for self-normalized partial sums","authors":"Muneya Matsui , Thomas Mikosch , Olivier Wintenberger","doi":"10.1016/j.spa.2025.104810","DOIUrl":"10.1016/j.spa.2025.104810","url":null,"abstract":"<div><div>We consider a regularly varyingstationary sequenceof random variables <span><math><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></math></span> with tail index <span><math><mrow><mi>α</mi><mo><</mo><mn>2</mn></mrow></math></span>. For this sequence we study the joint convergenceof sums, <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-type moduli and maxima. We focus on ratio statistics, including the studentized sums and sums normalized by the corresponding maxima, and study the existence of moments for the limit ratios. We consider particular examples of processes <span><math><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></math></span> whose limit ratios possess all moments as in the iid setting. But, in contrast to the latter situation, there also exist dependent sequences <span><math><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></math></span> where certain moments of the limit ratio are infinite. This phenomenon results from extremal clusters in the sequence.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104810"},"PeriodicalIF":1.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145418568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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