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Global maximum principle for partially observed risk-sensitive progressive optimal control of FBSDE with Poisson jumps 带泊松跳的FBSDE部分可观测风险敏感渐进最优控制的全局极大原理
IF 1.2 2区 数学
Stochastic Processes and their Applications Pub Date : 2026-05-01 Epub Date: 2026-01-07 DOI: 10.1016/j.spa.2026.104870
Jingtao Lin, Jingtao Shi
{"title":"Global maximum principle for partially observed risk-sensitive progressive optimal control of FBSDE with Poisson jumps","authors":"Jingtao Lin,&nbsp;Jingtao Shi","doi":"10.1016/j.spa.2026.104870","DOIUrl":"10.1016/j.spa.2026.104870","url":null,"abstract":"<div><div>This paper is concerned with one kind of partially observed progressive optimal control problems of coupled forward-backward stochastic systems driven by both Brownian motion and Poisson random measure with risk-sensitive criteria. The control domain is not necessarily convex, and the control variable can enters into all the coefficients. The observation equation also has correlated noises with the state equation. Under the Poisson jump setting, the original problem is equivalent to a stochastic recursive optimal control problem of a forward-backward system with quadratic-exponential generator. In order to establish the first- and second-order variations, some new techniques are introduced to overcome difficulties caused by the quadratic-exponential feature. A new global stochastic maximum principle is deduced. As an application, a risk-sensitive optimal investment problem with factor model is studied. Moreover, the risk-sensitive stochastic filtering problem is studied, which involves both Brownian and Poissonian correlated noises. A modified Zakai equation is obtained.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104870"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978771","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
Stretched non-local Pearson diffusions 拉伸非局部皮尔逊扩散
IF 1.2 2区 数学
Stochastic Processes and their Applications Pub Date : 2026-05-01 Epub Date: 2025-12-23 DOI: 10.1016/j.spa.2025.104854
Luisa Beghin , Nikolai Leonenko , Ivan Papić , Jayme Vaz
{"title":"Stretched non-local Pearson diffusions","authors":"Luisa Beghin ,&nbsp;Nikolai Leonenko ,&nbsp;Ivan Papić ,&nbsp;Jayme Vaz","doi":"10.1016/j.spa.2025.104854","DOIUrl":"10.1016/j.spa.2025.104854","url":null,"abstract":"<div><div>We define a novel class of time-changed Pearson diffusions, termed stretched non-local Pearson diffusions, where the stochastic time-change model has the Kilbas-Saigo function as its Laplace transform. Moreover, we introduce a stretched variant of the Caputo fractional derivative and prove that its eigenfunction is, in fact, the Kilbas-Saigo function. Furthermore, we solve fractional Cauchy problems involving the generator of the Pearson diffusion and the Fokker-Planck operator, providing both analytic and stochastic solutions, which connect the newly defined process and fractional operator with the Kilbas-Saigo function. We also prove that stretched non-local Pearson diffusions share the same limiting distributions as their standard counterparts. Finally, we investigate fractional hyperbolic Cauchy problems for Pearson diffusions, which resemble time-fractional telegraph equations, and provide both analytical and stochastic solutions. As a byproduct of our analysis, we derive a novel representation and an asymptotic formula for the Kilbas-Saigo function with complex arguments, which, to the best of our knowledge, are not currently available in the existing literature.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104854"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145847611","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
Purification of quantum trajectories in infinite dimensions 无限维量子轨迹的净化
IF 1.2 2区 数学
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
{"title":"Purification of quantum trajectories in infinite dimensions","authors":"Federico Girotti,&nbsp;Alessandro Vitale","doi":"10.1016/j.spa.2026.104889","DOIUrl":"10.1016/j.spa.2026.104889","url":null,"abstract":"<div><div>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 (<em>Infin. Dimens. Anal. Quantum Probab. Relat. Top.</em>, 06(02), 223-243, 2003 and <em>IMS Lectures Notes-Monograph Series</em>, 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.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104889"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023273","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
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
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
{"title":"The multi-level friendship paradox for sparse random graphs","authors":"Rajat Subhra Hazra,&nbsp;Frank den Hollander,&nbsp;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
Stochastic Processes and their Applications Pub Date : 2026-05-01 Epub Date: 2026-01-29 DOI: 10.1016/j.spa.2026.104893
Kazuo Yamazaki
{"title":"Remarks on the two-dimensional magnetohydrodynamics system forced by space-time white noise","authors":"Kazuo Yamazaki","doi":"10.1016/j.spa.2026.104893","DOIUrl":"10.1016/j.spa.2026.104893","url":null,"abstract":"<div><div>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., <strong>196</strong>, 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, <strong>10</strong>, 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.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104893"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146173744","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
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
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
{"title":"On stochastic partial differential equations and their applications to derivative pricing through a conditional Feynman-Kac formula","authors":"Kaustav Das ,&nbsp;Ivan Guo ,&nbsp;Grégoire Loeper","doi":"10.1016/j.spa.2026.104886","DOIUrl":"10.1016/j.spa.2026.104886","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104886"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146173745","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
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
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
{"title":"Limiting behavior of invariant measures of fractional stochastic reaction-diffusion equations on expanding domains","authors":"Zhang Chen ,&nbsp;Bixiang Wang ,&nbsp;Dandan Yang","doi":"10.1016/j.spa.2026.104884","DOIUrl":"10.1016/j.spa.2026.104884","url":null,"abstract":"<div><div>This paper is concerned with the limiting behavior of the fractional stochastic reaction-diffusion equations defined in a sequence <span><math><msubsup><mrow><mo>{</mo><msub><mi>O</mi><mi>k</mi></msub><mo>}</mo></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>∞</mi></msubsup></math></span> of open balls of radius <em>k</em> in <span><math><msup><mi>R</mi><mi>n</mi></msup></math></span>. Under certain conditions, we prove that every weak limit point of invariant measures of the equations defined in <em>O<sub>k</sub></em> must be an invariant measure of the equation defined on <span><math><msup><mi>R</mi><mi>n</mi></msup></math></span> as <em>k</em> → ∞. We also prove the convergence of invariant measures of the equations in <em>O<sub>k</sub></em> in terms of the Wasserstein metric and derive the rate of such convergence as <em>k</em> → ∞. The uniform tail-ends estimates of solutions are employed to overcome the non-compactness of Sobolev embeddings on <span><math><msup><mi>R</mi><mi>n</mi></msup></math></span>.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104884"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023260","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
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
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
{"title":"Reflected backward stochastic differential equations with rough drivers","authors":"Hanwu Li ,&nbsp;Huilin Zhang ,&nbsp;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
Limit theorems for stochastic integrals with long memory processes 长记忆过程随机积分的极限定理
IF 1.2 2区 数学
Stochastic Processes and their Applications Pub Date : 2026-05-01 Epub Date: 2026-01-17 DOI: 10.1016/j.spa.2026.104888
Zhishui Hu , Hanying Liang , Qiying Wang
{"title":"Limit theorems for stochastic integrals with long memory processes","authors":"Zhishui Hu ,&nbsp;Hanying Liang ,&nbsp;Qiying Wang","doi":"10.1016/j.spa.2026.104888","DOIUrl":"10.1016/j.spa.2026.104888","url":null,"abstract":"<div><div>On the convergence to stochastic integrals, semi-martingale structure is imposed in most of previous literature. This semi-martingale structure is restrictive in many statistical and econometric applications, particularly in the field of cointegration. In this paper, we investigate the convergence to stochastic integrals beyond the semi-martingale structure. In particular, we consider the convergence of stochastic integrals with general linear process innovations, allowing for long memory, short memory and antipersistence processes in a unified framework.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104888"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023275","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
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
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
{"title":"On the distribution of the telegraph meander and its properties","authors":"A. Pedicone,&nbsp;E. Orsingher","doi":"10.1016/j.spa.2026.104887","DOIUrl":"10.1016/j.spa.2026.104887","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104887"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978768","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
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