Stochastic Processes and their Applications最新文献

英文中文

Moments of generalized fractional polynomial processes 广义分数阶多项式过程的矩

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-02-05 DOI: 10.1016/j.spa.2026.104901

Johannes Assefa, Martin Keller-Ressel

We derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse Lévy-subordinator. If the time change is inverse α-stable, the time-derivative of the Kolmogorov backward equation is replaced by a Caputo fractional derivative of order α, and we demonstrate that moments of such processes are computable, in a closed form, using matrix Mittag-Leffler functions. The same holds true for cross-moments in equilibrium, generalizing results of Leonenko, Meerschaert and Sikorskii from the one-dimensional diffusive case of second-order moments to the multivariate, jump-diffusive case of moments of arbitrary order. We show that also in this more general setting, fractional polynomial processes exhibit long-range dependence, with correlations decaying as a power law with exponent α.

我们导出了广义分数阶多项式过程的矩公式，即由一个逆l -从属子变时的多项式保持马尔可夫过程的矩公式。如果时间变化是α-逆稳定的，则将Kolmogorov后向方程的时间导数替换为α阶的Caputo分数阶导数，并证明了这种过程的矩可以用矩阵Mittag-Leffler函数以封闭形式计算。这同样适用于平衡中的交叉矩，将Leonenko， Meerschaert和Sikorskii的结果从二阶矩的一维扩散情况推广到任意阶矩的多元跳跃扩散情况。我们还表明，在这种更一般的设置中，分数阶多项式过程表现出长期依赖性，相关性随着指数α的幂律而衰减。

引用次数: 0

A new stochastic SIS-type modelling framework for analysing epidemic dynamics in continuous space 连续空间流行病动力学分析的一种新的随机sis型建模框架

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-30 DOI: 10.1016/j.spa.2026.104896

Apolline Louvet , Bastian Wiederhold

We propose a new stochastic epidemiological model defined in a continuous space of arbitrary dimension, based on SIS dynamics implemented in a spatial Λ-Fleming-Viot (SLFV) process. The model can be described by as little as three parameters, and is dual to a spatial branching process with competition linked to genealogies of infected individuals. Therefore, it is a possible modelling framework to develop computationally tractable inference tools for epidemics in a continuous space using demographic and genetic data.

We provide mathematical constructions of the process based on well-posed martingale problems as well as driving space-time Poisson point processes. With these devices and the duality relation in hand, we unveil some of the drivers of the transition between extinction and survival of the epidemic. In particular, we show that extinction is in large parts independent of the initial condition, and identify a strong candidate for the reproduction number R₀ of the epidemic in such a model.

基于空间Λ-Fleming-Viot （SLFV）过程中的SIS动力学，提出了一个定义在任意维连续空间中的随机流行病学模型。该模型可以用三个参数来描述，并且是双重的空间分支过程，与受感染个体的谱系相关的竞争。因此，利用人口统计和遗传数据为连续空间中的流行病开发计算上易于处理的推断工具是一种可能的建模框架。我们提供了基于适定鞅问题的过程的数学结构以及驱动时空泊松点过程。有了这些设备和二元关系，我们揭示了流行病在灭绝和生存之间过渡的一些驱动因素。特别是，我们表明灭绝在很大程度上与初始条件无关，并确定了该模型中流行病繁殖数R0的强候选值。

引用次数: 0

Purification of quantum trajectories in infinite dimensions 无限维量子轨迹的净化

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-16 DOI: 10.1016/j.spa.2026.104889

Federico Girotti, Alessandro Vitale

In this work we exhibit a class of examples that show that the characterization of purification of quantum trajectories in terms of ‘dark’ subspaces that was proved for finite dimensional systems (Infin. Dimens. Anal. Quantum Probab. Relat. Top., 06(02), 223-243, 2003 and IMS Lectures Notes-Monograph Series, 48, 252-261, 2006) fails to hold in infinite dimensional ones. Moreover, we prove that the new phenomenon emerging in our class of models and preventing purification to happen is the only new possibility that appears in infinite dimensional systems. Our proof strategy points out that the presence of new phenomena in infinite dimensional systems is due to the fact that the set of orthogonal projections is not sequentially compact. Having in mind this insight, we are able to prove that the finite dimensional result extends to a class of infinite dimensional models.

在这项工作中，我们展示了一类例子，这些例子表明，在有限维系统中，用“暗”子空间来描述量子轨迹的纯化是被证明的。Dimens。分析的。量子Probab。遗传代数。上面。(1)在无限维空间中不成立。(1)在无限维空间中不成立。(2)在无限维空间中不成立。此外，我们证明了在我们这类模型中出现的阻止净化发生的新现象是在无限维系统中出现的唯一新可能性。我们的证明策略指出在无限维系统中新现象的存在是由于正交投影的集合不是顺序紧致的。考虑到这一点，我们能够证明有限维的结果可以推广到一类无限维的模型。

引用次数: 0

The multi-level friendship paradox for sparse random graphs 稀疏随机图的多级友谊悖论

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-09 DOI: 10.1016/j.spa.2026.104873

Rajat Subhra Hazra, Frank den Hollander, Azadeh Parvaneh

In [1] we analysed the friendship paradox for sparse random graphs. For four classes of random graphs we characterised the empirical distribution of the friendship biases between vertices and their neighbours at distance 1, proving convergence as n → ∞ to a limiting distribution, with n the number of vertices, and identifying moments and tail exponents of the limiting distribution. In the present paper we look at the multi-level friendship bias between vertices and their neighbours at distance

k \in N

obtained via a k-step exploration according to a backtracking or a non-backtracking random walk. We identify the limit of the empirical distribution of the multi-level friendship biases as n → ∞ and/or k → ∞. We show that for non-backtracking exploration the two limits commute for a large class of sparse random graphs, including those that locally converge to a rooted Galton-Watson tree. In particular, we show that the same limit arises when k depends on n, i.e.,

k = k_{n}

, provided

\lim_{n \to \infty} k_{n} = \infty

under some mild conditions. We exhibit cases where the two limits do not commute and show the relevance of the mixing time of the exploration.

在b[1]中，我们分析了稀疏随机图的友谊悖论。对于四类随机图，我们描述了距离为1的顶点与其邻居之间的友谊偏差的经验分布，证明了收敛为n → ∞到具有n个顶点的极限分布，并识别了极限分布的矩和尾指数。在本文中，我们通过k步探索，根据回溯或非回溯随机漫步，研究距离k∈N的顶点与其邻居之间的多级友谊偏差。我们确定了多级友谊偏差的经验分布的极限为n → ∞和/或k → ∞。我们证明了对于非回溯探索的两个极限可交换的一大类稀疏随机图，包括那些局部收敛到有根的高尔顿-沃森树。特别地，我们证明了当k依赖于n时，即k=kn，在一些温和的条件下，假设limn→∞kn=∞，也会出现相同的极限。我们展示了两种极限不相适应的情况，并展示了勘探混合时间的相关性。

{"title":"The multi-level friendship paradox for sparse random graphs","authors":"Rajat Subhra Hazra, Frank den Hollander, Azadeh Parvaneh","doi":"10.1016/j.spa.2026.104873","DOIUrl":"10.1016/j.spa.2026.104873","url":null,"abstract":"<div><div>In [1] we analysed the friendship paradox for sparse random graphs. For four classes of random graphs we characterised the empirical distribution of the friendship biases between vertices and their neighbours at distance 1, proving convergence as <em>n</em> → ∞ to a limiting distribution, with <em>n</em> the number of vertices, and identifying moments and tail exponents of the limiting distribution. In the present paper we look at the multi-level friendship bias between vertices and their neighbours at distance <span><math><mrow><mi>k</mi><mo>∈</mo><mi>N</mi></mrow></math></span> obtained via a <em>k</em>-step exploration according to a backtracking or a non-backtracking random walk. We identify the limit of the empirical distribution of the multi-level friendship biases as <em>n</em> → ∞ and/or <em>k</em> → ∞. We show that for non-backtracking exploration the two limits commute for a large class of sparse random graphs, including those that locally converge to a rooted Galton-Watson tree. In particular, we show that the same limit arises when <em>k</em> depends on <em>n</em>, i.e., <span><math><mrow><mi>k</mi><mo>=</mo><msub><mi>k</mi><mi>n</mi></msub></mrow></math></span>, provided <span><math><mrow><msub><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></msub><msub><mi>k</mi><mi>n</mi></msub><mo>=</mo><mi>∞</mi></mrow></math></span> under some mild conditions. We exhibit cases where the two limits do not commute and show the relevance of the mixing time of the exploration.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104873"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978769","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}

引用次数: 0

Remarks on the two-dimensional magnetohydrodynamics system forced by space-time white noise 时空白噪声作用下二维磁流体动力学系统的评述

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-29 DOI: 10.1016/j.spa.2026.104893

Kazuo Yamazaki

We study the two-dimensional magnetohydrodynamics system forced by space-time white noise. Due to a lack of an explicit invariant measure, the approach of Da Prato and Debussche (2002, J. Funct. Anal., 196, pp. 180–210) on the Navier-Stokes equations does not seem to fit. We follow instead the approach of Hairer and Rosati (2024, Ann. PDE, 10, pp. 1–46), take advantage of the structure of Maxwell’s equation, such as anti-symmetry, to find an appropriate paracontrolled ansatz and many crucial cancellations, and prove the global-in-time existence and uniqueness of its solution.

研究了时空白噪声作用下的二维磁流体动力学系统。由于缺乏明确的不变测度，Da Prato和Debussche (2002， J. Funct。分析的。（第196页，第180-210页）关于Navier-Stokes方程似乎不合适。相反，我们遵循海勒和罗萨蒂(2024，安。PDE, 10, pp. 1-46)，利用麦克斯韦方程的反对称等结构，找到了一个合适的副控制解和许多关键的消去，并证明了其解的全局存在唯一性。

引用次数: 0

On stochastic partial differential equations and their applications to derivative pricing through a conditional Feynman-Kac formula 基于条件费曼-卡茨公式的随机偏微分方程及其在导数定价中的应用

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-16 DOI: 10.1016/j.spa.2026.104886

Kaustav Das , Ivan Guo , Grégoire Loeper

The price of a financial derivative can be expressed as an iterated conditional expectation, where the inner term conditions on the future of an auxiliary process. We show that this inner conditional expectation solves an SPDE (a ‘conditional Feynman-Kac formula’). The problem requires conditioning on a backward filtration generated by the noise of the auxiliary process and enlarged by its terminal value, leading us to search for a backward Brownian motion here. This adds a source of irregularity to the SPDE which we tackle with new techniques. Lastly, we establish a new class of mixed Monte-Carlo PDE numerical methods.

金融衍生品的价格可以表示为一个迭代的条件期望，其中的内部条款是对一个辅助过程的未来的条件。我们证明了这个内部条件期望解决了一个SPDE（一个“条件费曼-卡茨公式”）。这个问题需要对辅助过程的噪声产生的后向滤波进行调节，并将其终端值放大，从而使我们在这里寻找后向布朗运动。这给SPDE增加了一个不规范的来源，我们用新技术来解决这个问题。最后，我们建立了一类新的混合蒙特卡罗偏微分方程数值方法。

引用次数: 0

On the distribution of the telegraph meander and its properties 论电报弯曲的分布及其性质

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-14 DOI: 10.1016/j.spa.2026.104887

A. Pedicone, E. Orsingher

In this paper we study the telegraph meander, a random function obtained by conditioning the telegraph process to stay above the zero level. The finite dimensional distribution of the telegraph meander is derived by applying the reflection principle for the telegraph process and the Markovianity of the telegraph process with the velocity process. We show that the law of the telegraph meander at the end time is a solution to a hyperbolic equation, and we find the characteristic function and moments of any order. Finally, we prove that Brownian meander is the weak limit of the telegraph meander.

本文研究了电报迂回，这是一种通过使电报过程保持在零水平以上而得到的随机函数。利用电报过程的反射原理和电报过程与速度过程的马尔可夫性，导出了电报曲流的有限维分布。我们证明了终端时间的电报弯曲定律是一个双曲方程的解，并找到了任意阶的特征函数和矩。最后，我们证明了布朗弯曲是电报弯曲的弱极限。

引用次数: 0

Sharp Lq-convergence rate in p-Wasserstein distance for empirical measures of diffusion processes 扩散过程经验测度的p-Wasserstein距离的尖锐lq收敛速率

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-05 DOI: 10.1016/j.spa.2026.104869

Feng-Yu Wang , Bingyao Wu , Jie-Xiang Zhu

In this paper we study the long time behavior in Wasserstein distance for empirical measures of (non-symmetric) diffusion processes on a length space satisfying the Nash inequality, which in particular include the (reflecting) diffusion processes on a connected compact Riemannian manifold. As a general result, the sharp convergence rate in

L^{q} (P)

for the p-Wasserstein distance is derived uniformly in p ∈ [1, ∞) and q ∈ (0, ∞). A key novelty of our approach, compared to existing works, is the use of a Bernstein-type inequality for diffusion processes.

本文研究了满足Nash不等式的长度空间上（非对称）扩散过程的经验测度在Wasserstein距离上的长时间行为，特别是包括连通紧黎曼流形上的（反射）扩散过程。作为一般结果，在P ∈ [1，∞]和q ∈ （0,∞）中，一致地导出了P - wasserstein距离在Lq(P)中的急剧收敛速率。与现有的工作相比，我们的方法的一个关键新颖之处在于对扩散过程使用了伯恩斯坦型不等式。

引用次数: 0

Limiting behavior of invariant measures of fractional stochastic reaction-diffusion equations on expanding domains 扩展域上分数阶随机反应扩散方程不变测度的极限行为

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-14 DOI: 10.1016/j.spa.2026.104884

Zhang Chen , Bixiang Wang , Dandan Yang

This paper is concerned with the limiting behavior of the fractional stochastic reaction-diffusion equations defined in a sequence

{O_{k}}_{k = 1}^{\infty}

of open balls of radius k in

R^{n}

. Under certain conditions, we prove that every weak limit point of invariant measures of the equations defined in O_k must be an invariant measure of the equation defined on

R^{n}

as k → ∞. We also prove the convergence of invariant measures of the equations in O_k in terms of the Wasserstein metric and derive the rate of such convergence as k → ∞. The uniform tail-ends estimates of solutions are employed to overcome the non-compactness of Sobolev embeddings on

R^{n}

研究了在Rn中半径为k的开球序列{Ok}k=1∞上定义的分数阶随机反应扩散方程的极限行为。在一定条件下，我们证明了在Ok中定义的方程的不变测度的每一个弱极限点必须是在Rn上定义为k → ∞的方程的不变测度。我们还用Wasserstein度规证明了Ok中方程不变测度的收敛性，并导出了k → ∞的收敛率。采用均匀尾端估计来克服Rn上Sobolev嵌入的非紧性。

引用次数: 0

Reflected backward stochastic differential equations with rough drivers 反映逆向随机微分方程与粗糙的驱动器

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-10 DOI: 10.1016/j.spa.2026.104874

Hanwu Li , Huilin Zhang , Kuan Zhang

In this paper, we investigate reflected backward stochastic differential equations driven by rough paths (rough RBSDEs), which can be viewed as probabilistic representations of nonlinear rough partial differential equations (rough PDEs) or stochastic partial differential equations (SPDEs) with obstacles. Furthermore, we demonstrate that solutions to rough RBSDEs solve the corresponding optimal stopping problems within a rough framework. This development provides effective and practical tools for pricing American options in the context of the rough volatility model, thus playing a crucial role in advancing the understanding and application of option pricing in complex market regimes.

The well-posedness of rough RBSDEs is established using a variant of the Doss-Sussmann transformation. Moreover, we show that rough RBSDEs can be approximated by a sequence of penalized BSDEs with rough drivers. For applications, we first develop the viscosity solution theory for rough PDEs with obstacles via rough RBSDEs. Second, we solve the corresponding optimal stopping problem and establish its connection with an American option pricing problem in the rough path setting.

本文研究了由粗糙路径驱动的反射后向随机微分方程（rough RBSDEs），它可以看作是非线性粗糙偏微分方程（rough PDEs）或随机偏微分方程（SPDEs）的概率表示。此外，我们证明了粗糙RBSDEs的解在粗糙框架内解决了相应的最优停止问题。这一发展为粗糙波动率模型下的美式期权定价提供了有效和实用的工具，从而对复杂市场机制下期权定价的理解和应用起着至关重要的作用。利用Doss-Sussmann变换的一种变体，建立了粗糙RBSDEs的适定性。此外，我们还证明了粗糙的RBSDEs可以用带有粗糙驱动器的惩罚BSDEs序列来近似。在应用方面，我们首先通过粗糙的RBSDEs建立了具有障碍物的粗糙PDEs的粘度解理论。其次，求解了相应的最优停止问题，并将其与粗糙路径设置下的美式期权定价问题建立联系。

{"title":"Reflected backward stochastic differential equations with rough drivers","authors":"Hanwu Li , Huilin Zhang , Kuan Zhang","doi":"10.1016/j.spa.2026.104874","DOIUrl":"10.1016/j.spa.2026.104874","url":null,"abstract":"<div><div>In this paper, we investigate reflected backward stochastic differential equations driven by rough paths (rough RBSDEs), which can be viewed as probabilistic representations of nonlinear rough partial differential equations (rough PDEs) or stochastic partial differential equations (SPDEs) with obstacles. Furthermore, we demonstrate that solutions to rough RBSDEs solve the corresponding optimal stopping problems within a rough framework. This development provides effective and practical tools for pricing American options in the context of the rough volatility model, thus playing a crucial role in advancing the understanding and application of option pricing in complex market regimes.</div><div>The well-posedness of rough RBSDEs is established using a variant of the Doss-Sussmann transformation. Moreover, we show that rough RBSDEs can be approximated by a sequence of penalized BSDEs with rough drivers. For applications, we first develop the viscosity solution theory for rough PDEs with obstacles via rough RBSDEs. Second, we solve the corresponding optimal stopping problem and establish its connection with an American option pricing problem in the rough path setting.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104874"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023274","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}

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Stochastic Processes and their Applications

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀