Pub Date : 2025-10-22DOI: 10.1016/j.spa.2025.104808
Benny Avelin , Tuomo Kuusi , Patrik Nummi , Eero Saksman , Jonas M. Tölle , Lauri Viitasaari
We study unique solvability for one-dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove well-posedness for Dirichlet, Neumann and periodic boundary data and the initial value problem, covering the cases of both the Wick renormalization of the diffusion and of point-wise multiplication. We provide explicit representations for the solutions in both cases, characterized by the -transform and the Gaussian multiplicative chaos measure.
{"title":"1D stochastic pressure equation with log-correlated Gaussian coefficients","authors":"Benny Avelin , Tuomo Kuusi , Patrik Nummi , Eero Saksman , Jonas M. Tölle , Lauri Viitasaari","doi":"10.1016/j.spa.2025.104808","DOIUrl":"10.1016/j.spa.2025.104808","url":null,"abstract":"<div><div>We study unique solvability for one-dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove well-posedness for Dirichlet, Neumann and periodic boundary data and the initial value problem, covering the cases of both the Wick renormalization of the diffusion and of point-wise multiplication. We provide explicit representations for the solutions in both cases, characterized by the <span><math><mi>S</mi></math></span>-transform and the Gaussian multiplicative chaos measure.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104808"},"PeriodicalIF":1.2,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364477","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 : 2025-10-21DOI: 10.1016/j.spa.2025.104807
Shukai Chen , Rongjuan Fang , Lina Ji , Jian Wang
We establish the exponential ergodicity in a weighted total variation distance of continuous-state branching processes with immigration in random environments with competition and catastrophes, under a Lyapunov-type condition and other mild assumptions. The proof is based on a Markov coupling process along with some delicate estimates for the associated coupling generator. In particular, the main result indicates whether and how the competition mechanism, the random environment and the catastrophe could balance the branching mechanism respectively to guarantee the exponential ergodicity of the processes.
{"title":"Exponential ergodicity of CBIRE-processes with competition and catastrophes","authors":"Shukai Chen , Rongjuan Fang , Lina Ji , Jian Wang","doi":"10.1016/j.spa.2025.104807","DOIUrl":"10.1016/j.spa.2025.104807","url":null,"abstract":"<div><div>We establish the exponential ergodicity in a weighted total variation distance of continuous-state branching processes with immigration in random environments with competition and catastrophes, under a Lyapunov-type condition and other mild assumptions. The proof is based on a Markov coupling process along with some delicate estimates for the associated coupling generator. In particular, the main result indicates whether and how the competition mechanism, the random environment and the catastrophe could balance the branching mechanism respectively to guarantee the exponential ergodicity of the processes.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104807"},"PeriodicalIF":1.2,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364476","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 : 2025-10-21DOI: 10.1016/j.spa.2025.104806
Oskar Eklund, Annika Lang, Moritz Schauer
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the theory of enlargement of filtrations to show that the conditional process has an additional drift term derived from the backward filtering distribution that is moving or guiding the process towards the observations. This term is intractable, but its effect can be equally introduced by replacing it with a heuristic, where importance weights correct for the discrepancy. From this Markov Chain Monte Carlo and sequential Monte Carlo algorithms are derived to sample from the smoothing distribution. The choice of the guiding heuristic is discussed from an optimal control perspective and evaluated. The results are tested numerically on a stochastic differential equation for reaction–diffusion.
{"title":"Guided smoothing and control for diffusion processes","authors":"Oskar Eklund, Annika Lang, Moritz Schauer","doi":"10.1016/j.spa.2025.104806","DOIUrl":"10.1016/j.spa.2025.104806","url":null,"abstract":"<div><div>The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the theory of enlargement of filtrations to show that the conditional process has an additional drift term derived from the backward filtering distribution that is moving or guiding the process towards the observations. This term is intractable, but its effect can be equally introduced by replacing it with a heuristic, where importance weights correct for the discrepancy. From this Markov Chain Monte Carlo and sequential Monte Carlo algorithms are derived to sample from the smoothing distribution. The choice of the guiding heuristic is discussed from an optimal control perspective and evaluated. The results are tested numerically on a stochastic differential equation for reaction–diffusion.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104806"},"PeriodicalIF":1.2,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145467272","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 : 2025-10-21DOI: 10.1016/j.spa.2025.104811
David Clancy Jr.
Enriquez et al. (2025) have established process-level fluctuations for the giant of the dynamic Erdős–Rényi random graph above criticality and show that the limit is a centered Gaussian process with continuous sample paths. A random walk proof was recently obtained by Corujo et al. (2024). We show that a similar result holds for rank-one inhomogeneous models whenever the empirical weight distribution converges to a limit and its second moment converges as well.
Enriquez et al.（2025）建立了临界以上动态Erdős-Rényi随机图的巨型过程级波动，并表明其极限是一个样本路径连续的中心高斯过程。Corujo et al.（2024）最近获得了一个随机行走证明。我们表明，当经验权重分布收敛到一个极限并且其第二矩也收敛时，对于秩一非齐次模型也有类似的结果。
{"title":"Fluctuations of the giant of Poisson random graphs","authors":"David Clancy Jr.","doi":"10.1016/j.spa.2025.104811","DOIUrl":"10.1016/j.spa.2025.104811","url":null,"abstract":"<div><div>Enriquez et al. (2025) have established process-level fluctuations for the giant of the dynamic Erdős–Rényi random graph above criticality and show that the limit is a centered Gaussian process with continuous sample paths. A random walk proof was recently obtained by Corujo et al. (2024). We show that a similar result holds for rank-one inhomogeneous models whenever the empirical weight distribution converges to a limit and its second moment converges as well.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104811"},"PeriodicalIF":1.2,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145418570","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 : 2025-10-21DOI: 10.1016/j.spa.2025.104809
Kou Fujimori , Koji Tsukuda
We propose a two-step estimation procedure for stochastic process models with high-dimensional parameters of interest under heteroskedasticity. In low-dimensional settings, when a consistent estimator for a nuisance parameter that characterizes the conditional variance is available, one can construct an asymptotically normal estimator for the parameter of interest under appropriate conditions. Motivated by this fact, we extend the idea to high-dimensional settings. We first establish variable selection via the Dantzig selector, and then combine this with consistent estimation of the nuisance parameter to develop a two-step procedure that yields an asymptotically normal estimator. Our framework accommodates infinite-dimensional nuisance parameters in the conditional variance term. Therefore, this study extends sparse estimation methods to a broader class of stochastic process models. Applications to ergodic time series models, including integer-valued autoregressive models and ergodic diffusion processes, are presented.
{"title":"Two-step estimations via the Dantzig selector for models of stochastic processes with high-dimensional parameters","authors":"Kou Fujimori , Koji Tsukuda","doi":"10.1016/j.spa.2025.104809","DOIUrl":"10.1016/j.spa.2025.104809","url":null,"abstract":"<div><div>We propose<!--> <!-->a<!--> <!-->two-step estimation procedure for stochastic process models with high-dimensional parameters of interest under heteroskedasticity. In low-dimensional settings, when a consistent estimator for a nuisance parameter that characterizes the conditional variance is available, one can construct an asymptotically normal estimator for the parameter of interest under appropriate conditions. Motivated by this fact, we extend the idea to high-dimensional settings. We first establish variable selection via the Dantzig selector, and then combine this with consistent estimation of the nuisance parameter to develop a two-step procedure that yields an asymptotically normal estimator. Our framework accommodates infinite-dimensional nuisance parameters in the conditional variance term. Therefore, this study extends sparse estimation methods to a broader class of stochastic process models. Applications to ergodic time series models, including integer-valued autoregressive models and ergodic diffusion processes, are presented.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104809"},"PeriodicalIF":1.2,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364474","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 : 2025-10-21DOI: 10.1016/j.spa.2025.104790
Jakob E. Björnberg , Cécile Mailler
We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional “doubling events” when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size of this tree at large times, its degree distribution, and its height profile. We also prove a lower bound for its height. Because of the doubling events that affect the tree globally, the proofs are all much more intricate than in the case of the random recursive tree in which the growing operation is always local.
{"title":"A random recursive tree model with doubling events","authors":"Jakob E. Björnberg , Cécile Mailler","doi":"10.1016/j.spa.2025.104790","DOIUrl":"10.1016/j.spa.2025.104790","url":null,"abstract":"<div><div>We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional “doubling events” when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size of this tree at large times, its degree distribution, and its height profile. We also prove a lower bound for its height. Because of the doubling events that affect the tree globally, the proofs are all much more intricate than in the case of the random recursive tree in which the growing operation is always local.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104790"},"PeriodicalIF":1.2,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364478","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 : 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":"2025-10-20","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 : 2025-10-20DOI: 10.1016/j.spa.2025.104796
Antonio Galves , Fernando A. Najman , Marcela Svarc , Claudia D. Vargas
We introduce a new clustering procedure for functional data analysis which can classify independent sets of functional samples by their probabilistic law, i.e. that aims to assign data sets to the same cluster if and only if the data were generated with the same underlying distribution. This method has the virtue of being non-supervised and non-parametric, allowing for exploratory investigation with few assumptions about the data. We also present rigorous finite bounds that give us the effect of the number of samples in each dataset on the classification. We also provide an objective heuristic that consistently selects the best partition in a data-driven manner. We show the performance of the method by clustering simulated datasets generated with different distributions.
{"title":"Clustering functional data sets by law","authors":"Antonio Galves , Fernando A. Najman , Marcela Svarc , Claudia D. Vargas","doi":"10.1016/j.spa.2025.104796","DOIUrl":"10.1016/j.spa.2025.104796","url":null,"abstract":"<div><div>We introduce a new clustering procedure for functional data analysis which can classify independent sets of functional samples by their probabilistic law, i.e. that aims to assign data sets to the same cluster if and only if the data were generated with the same underlying distribution. This method has the virtue of being non-supervised and non-parametric, allowing for exploratory investigation with few assumptions about the data. We also present rigorous finite bounds that give us the effect of the number of samples in each dataset on the classification. We also provide an objective heuristic that consistently selects the best partition in a data-driven manner. We show the performance of the method by clustering simulated datasets generated with different distributions.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104796"},"PeriodicalIF":1.2,"publicationDate":"2025-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145418566","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 : 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":"2025-10-18","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 : 2025-10-18DOI: 10.1016/j.spa.2025.104803
Attila Lovas
Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the functional central limit theorem, are known for weakly dependent variables. We demonstrate the transfer of mixing properties from the exogenous regressor to the response via coupling arguments. Additionally, we study Markov chains in random environments with drift and minorization conditions, even under non-stationary environments with favorable mixing properties, and apply this framework to single-server queuing models.
{"title":"Transition of α-mixing in random iterations with applications in queuing theory","authors":"Attila Lovas","doi":"10.1016/j.spa.2025.104803","DOIUrl":"10.1016/j.spa.2025.104803","url":null,"abstract":"<div><div>Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the functional central limit theorem, are known for weakly dependent variables. We demonstrate the transfer of mixing properties from the exogenous regressor to the response via coupling arguments. Additionally, we study Markov chains in random environments with drift and minorization conditions, even under non-stationary environments with favorable mixing properties, and apply this framework to single-server queuing models.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"192 ","pages":"Article 104803"},"PeriodicalIF":1.2,"publicationDate":"2025-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364469","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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