Stochastic Processes and their Applications最新文献

Duality for some models of epidemic spreading 某些流行病传播模型的对偶性

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-27 DOI: 10.1016/j.spa.2025.104773

C. Franceschini , E. Saada , G.M. Schütz , S. Velasco

{"title":"Duality for some models of epidemic spreading","authors":"C. Franceschini , E. Saada , G.M. Schütz , S. Velasco","doi":"10.1016/j.spa.2025.104773","DOIUrl":"10.1016/j.spa.2025.104773","url":null,"abstract":"<div><div>We examine the role of boundaries and the structure of nontrivial duality functions for three non-conservative interacting particle systems in one dimension that model epidemic spreading: (i) the diffusive contact process (DCP), (ii) a model that we introduce and call generalized diffusive contact process (GDCP), both in finite volume in contact with boundary reservoirs, i.e., with open boundaries, and (iii) the susceptible–infectious–recovered (SIR) model on <span><math><mi>Z</mi></math></span>. We establish duality relations for each system through an analytical approach. It turns out that with open boundaries self-duality breaks down and qualitatively different properties compared to closed boundaries (i.e., finite volume without reservoirs) arise: Both the DCP and GDCP are ergodic but no longer absorbing, while the respective dual processes are absorbing but not ergodic. We provide expressions for the stationary correlation functions in terms of the dual absorption probabilities. We perform explicit computations for a small sized DCP, and for arbitrary size in a particular setting of the GDCP. The duality function is factorized for the DCP and GDCP, contrary to the SIR model for which the duality relation is nonlocal and yields an explicit expression of the time evolution of some specific correlation functions, describing the time decay of the sizes of clusters of susceptible individuals.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"191 ","pages":"Article 104773"},"PeriodicalIF":1.2,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222192","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

Deviation inequalities for contractive infinite memory processes 收缩无限存储过程的偏差不等式

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-25 DOI: 10.1016/j.spa.2025.104778

Paul Doukhan , Xiequan Fan

引用次数: 0

Holomorphic jump-diffusions 全纯jump-diffusions

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-24 DOI: 10.1016/j.spa.2025.104781

Christa Cuchiero , Francesca Primavera , Sara Svaluto-Ferro

引用次数: 0

Swarm dynamics for global optimization on finite sets 有限集上全局优化的群体动力学

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-22 DOI: 10.1016/j.spa.2025.104780

Nhat-Thang Le , Laurent Miclo

{"title":"Swarm dynamics for global optimization on finite sets","authors":"Nhat-Thang Le , Laurent Miclo","doi":"10.1016/j.spa.2025.104780","DOIUrl":"10.1016/j.spa.2025.104780","url":null,"abstract":"<div><div>Consider the global optimisation of a function <span><math><mi>U</mi></math></span> defined on a finite set <span><math><mi>V</mi></math></span> endowed with an irreducible and reversible Markov generator. By integration, we extend <span><math><mi>U</mi></math></span> to the set <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>V</mi><mo>)</mo></mrow></mrow></math></span> of probability distributions on <span><math><mi>V</mi></math></span> and we penalize it with a time-dependent generalized entropy functional. Endowing <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>V</mi><mo>)</mo></mrow></mrow></math></span> with a Maas’ Wasserstein-type Riemannian structure enables us to consider an associated time-inhomogeneous gradient descent algorithm. There are several ways to interpret this <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>V</mi><mo>)</mo></mrow></mrow></math></span>-valued dynamical system as the time-marginal laws of a time-inhomogeneous non-linear Markov process taking values in <span><math><mi>V</mi></math></span>, each of them allowing for interacting particle approximations. This procedure extends to the discrete framework the continuous state space swarm algorithm approach of Bolte et al. (2023), but here we go further by considering more general generalized entropy functionals for which functional inequalities can be proven. Thus in the full generality of the above finite framework, we give conditions on the underlying time dependence ensuring the convergence of the algorithm toward laws supported by the set of global minima of <span><math><mi>U</mi></math></span>. Numerical simulations illustrate that one has to be careful about the choice of the time-inhomogeneous non-linear Markov process interpretation.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"191 ","pages":"Article 104780"},"PeriodicalIF":1.2,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222193","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

Optimal control of the nonlinear stochastic Fokker–Planck equation 非线性随机Fokker-Planck方程的最优控制

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-17 DOI: 10.1016/j.spa.2025.104774

Ben Hambly , Philipp Jettkant

{"title":"Optimal control of the nonlinear stochastic Fokker–Planck equation","authors":"Ben Hambly , Philipp Jettkant","doi":"10.1016/j.spa.2025.104774","DOIUrl":"10.1016/j.spa.2025.104774","url":null,"abstract":"<div><div>We consider a control problem for the nonlinear stochastic Fokker–Planck equation. This equation describes the evolution of the distribution of nonlocally interacting particles affected by a common source of noise. The system is directed by a controller that acts on the drift term with the goal of minimising a cost functional. We establish the well-posedness of the state equation, prove the existence of optimal controls, and formulate a stochastic maximum principle (SMP) that provides necessary and sufficient optimality conditions for the control problem. The adjoint process arising in the SMP is characterised by a nonlocal (semi)linear backward SPDE for which we study existence and uniqueness. We also rigorously connect the control problem for the nonlinear stochastic Fokker–Planck equation to the control of the corresponding McKean–Vlasov SDE that describes the motion of a representative particle. Our work extends existing results for the control of the Fokker–Planck equation to nonlinear and stochastic dynamics. In particular, the sufficient SMP, which we obtain by exploiting the special structure of the Fokker–Planck equation, seems to be novel even in the linear deterministic setting. We illustrate our results with an application to a model of government interventions in financial systems, supplemented by numerical illustrations.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"191 ","pages":"Article 104774"},"PeriodicalIF":1.2,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120730","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

Convergence of adapted smoothed empirical measures 自适应平滑经验测度的收敛性

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-17 DOI: 10.1016/j.spa.2025.104775

Songyan Hou

{"title":"Convergence of adapted smoothed empirical measures","authors":"Songyan Hou","doi":"10.1016/j.spa.2025.104775","DOIUrl":"10.1016/j.spa.2025.104775","url":null,"abstract":"<div><div>The <em>adapted Wasserstein distance</em> (<span><math><mi>AW</mi></math></span>-distance) controls the calibration errors of optimal values in various stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. However, statistical aspects of the <span><math><mi>AW</mi></math></span>-distance are bottlenecked by the failure of <em>empirical measures</em> (<em>Emp</em>) to converge under this distance. Kernel smoothing and adapted projection have been introduced to construct converging substitutes of empirical measures, known respectively as <em>smoothed empirical measures</em> (<span><math><mi>S</mi></math></span>-<em>Emp</em>) and <em>adapted empirical measures</em> (<span><math><mi>A</mi></math></span>-<em>Emp</em>). However, both approaches have limitations. Specifically, <span><math><mi>S</mi></math></span>-<em>Emp</em> lack comprehensive convergence results, whereas <span><math><mi>A</mi></math></span>-<em>Emp</em> in practical applications lead to fewer distinct samples compared to standard empirical measures.</div><div>In this work, we address both of the aforementioned issues. First, we develop comprehensive convergence results of <span><math><mi>S</mi></math></span>-<em>Emp</em>. We then introduce a smoothed version for <span><math><mi>A</mi></math></span>-<em>Emp</em>, which provide as many distinct samples as desired. We refer them as <span><math><mi>AS</mi></math></span>-<em>Emp</em> and establish their convergence in mean, deviation and almost sure convergence. The convergence estimation incorporates two results: the empirical analysis of the <em>smoothed adapted Wasserstein distance</em> (<span><math><msup><mrow><mi>AW</mi></mrow><mrow><mrow><mo>(</mo><mi>σ</mi><mo>)</mo></mrow></mrow></msup></math></span>-distance) and its bandwidth effects. Both results are novel and their proof techniques could be of independent interest.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"191 ","pages":"Article 104775"},"PeriodicalIF":1.2,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108595","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

Mixing time and cutoff for the k-SPEP k-SPEP的混合时间和截止时间

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-16 DOI: 10.1016/j.spa.2025.104776

Eyob Tsegaye

引用次数: 0

Reflected BSDE driven by a marked point process with a convex/concave generator 反射BSDE驱动的标记点过程与凸/凹生成器

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-16 DOI: 10.1016/j.spa.2025.104777

Zihao Gu , Yiqing Lin , Kun Xu

引用次数: 0

A tamed Euler scheme for SDEs with non-locally integrable drift coefficient 漂移系数非局部可积的SDEs的驯服欧拉格式

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-16 DOI: 10.1016/j.spa.2025.104772

Tim Johnston , Sotirios Sabanis

引用次数: 0

Spectral gap for the stochastic exchange model 随机交换模型的谱隙

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-12 DOI: 10.1016/j.spa.2025.104769

Eric A. Carlen , Gustavo Posta , Imre Péter Tóth

引用次数: 0