Stochastic Processes and their Applications最新文献_第2页

Scaling limit and large deviation for 3D globally modified stochastic Navier–Stokes equations with transport noise 含输运噪声的三维全局修正随机Navier-Stokes方程的尺度极限和大偏差

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-12 DOI: 10.1016/j.spa.2025.104770

Chang Liu , Dejun Luo

引用次数: 0

One-sided Markov additive processes with lattice and non-lattice increments 具有格和非格增量的单侧马尔可夫加性过程

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-11 DOI: 10.1016/j.spa.2025.104771

Jevgenijs Ivanovs , Guy Latouche , Peter Taylor

{"title":"One-sided Markov additive processes with lattice and non-lattice increments","authors":"Jevgenijs Ivanovs , Guy Latouche , Peter Taylor","doi":"10.1016/j.spa.2025.104771","DOIUrl":"10.1016/j.spa.2025.104771","url":null,"abstract":"<div><div>Dating from the work of Neuts in the 1980s, the field of matrix-analytic methods has been developed to analyse discrete or continuous-time Markov chains with a two-dimensional state space in which the increment of a <em>level</em> variable is governed by an auxiliary <em>phase</em> variable. More recently, matrix-analytic techniques have been applied to general Markov additive models with a finite phase space. The basic assumption underlying these developments is that the process is skip-free (in the case of QBDs or fluid queues) or that it is <em>one-sided</em>, that is it is jump-free in one direction.</div><div>From the Markov additive perspective, traditional matrix-analytic models can be viewed as special cases: for M/G/1 and GI/M/1-type Markov chains, increments in the level are constrained to be <em>lattice</em> random variables and for fluid queues, they have to be piecewise linear.</div><div>In this paper we discuss one-sided lattice and non-lattice Markov additive processes in parallel. Results that are standard in one tradition are interpreted in the other, and new perspectives emerge. In particular, using three fundamental matrices, we address hitting, two-sided exit, and creeping probabilities.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104771"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145104280","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

A+A→A, B+A→A +一个→A、B +一个→

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-08 DOI: 10.1016/j.spa.2025.104766

Roger Tribe, Oleg Zaboronski

引用次数: 0

Central limit theorems associated with the hierarchical Dirichlet process 与分层狄利克雷过程相关的中心极限定理

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-03 DOI: 10.1016/j.spa.2025.104767

Shui Feng, J.E. Paguyo

引用次数: 0

Parameter estimation in hyperbolic linear SPDEs from multiple measurements 双曲线性spde的参数估计

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-09-03 DOI: 10.1016/j.spa.2025.104768

Anton Tiepner , Eric Ziebell

引用次数: 0

Mirror descent for stochastic control problems with measure-valued controls 具有测量值控制的随机控制问题的镜像下降

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-08-28 DOI: 10.1016/j.spa.2025.104765

Bekzhan Kerimkulov , David Šiška , Łukasz Szpruch , Yufei Zhang

{"title":"Mirror descent for stochastic control problems with measure-valued controls","authors":"Bekzhan Kerimkulov , David Šiška , Łukasz Szpruch , Yufei Zhang","doi":"10.1016/j.spa.2025.104765","DOIUrl":"10.1016/j.spa.2025.104765","url":null,"abstract":"<div><div>This paper studies the convergence of the mirror descent algorithm for finite horizon stochastic control problems with measure-valued control processes. The control objective involves a convex regularisation function, denoted as <span><math><mi>h</mi></math></span>, with regularisation strength determined by the weight <span><math><mrow><mi>τ</mi><mo>≥</mo><mn>0</mn></mrow></math></span>. The setting covers regularised relaxed control problems. Under suitable conditions, we establish the relative smoothness and convexity of the control objective with respect to the Bregman divergence of <span><math><mi>h</mi></math></span>, and prove linear convergence of the algorithm for <span><math><mrow><mi>τ</mi><mo>=</mo><mn>0</mn></mrow></math></span> and exponential convergence for <span><math><mrow><mi>τ</mi><mo>></mo><mn>0</mn></mrow></math></span>. The results apply to common regularisers including relative entropy, <span><math><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-divergence, and entropic Wasserstein costs. This validates recent reinforcement learning heuristics that adding regularisation accelerates the convergence of gradient methods. The proof exploits careful regularity estimates of backward stochastic differential equations in the bounded mean oscillation norm.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104765"},"PeriodicalIF":1.2,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144916858","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

Essential barrier height and a probabilistic approach in characterizing potential landscape 基本屏障高度和潜在景观特征的概率方法

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-08-22 DOI: 10.1016/j.spa.2025.104763

Yao Li , Molei Tao , Shirou Wang

{"title":"Essential barrier height and a probabilistic approach in characterizing potential landscape","authors":"Yao Li , Molei Tao , Shirou Wang","doi":"10.1016/j.spa.2025.104763","DOIUrl":"10.1016/j.spa.2025.104763","url":null,"abstract":"<div><div>This paper proposes a probabilistic approach to investigate the shape of landscapes of multi-dimensional potential functions. Under a suitable coupling scheme, two copies of the overdamped Langevin dynamics associated with the potential function are coupled, and the coupling times are collected. Assuming a set of intuitive yet technically challenging conditions on the coupling scheme, it is shown that the tail distributions of the coupling times exhibit qualitatively different dependencies on the noise magnitude for single-well versus multi-well potential functions. More specifically, for convex single-well potentials, the negative tail exponent of the coupling time distribution is uniformly bounded away from zero by the convexity parameter and is independent of the noise magnitude. In contrast, for multi-well potentials, the negative tail exponent decreases exponentially as the noise vanishes, with the decay rate governed by the <em>essential barrier height</em>, a quantity introduced in this paper to characterize the non-convex nature of the potential function. Numerical investigations are conducted for a variety of examples, including the Rosenbrock function, interacting particle systems, and loss functions arising in artificial neural networks. These examples not only illustrate the theoretical results in various contexts but also provide crucial numerical validation of the conjectured assumptions, which are essential to the theoretical analysis yet lie beyond the reach of standard technical tools.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104763"},"PeriodicalIF":1.2,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907766","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

Parallelized midpoint randomization for Langevin Monte Carlo 朗格万蒙特卡罗的并行中点随机化

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-08-21 DOI: 10.1016/j.spa.2025.104764

Lu Yu , Arnak Dalalyan

引用次数: 0

Rough differential equations in the flow approach 流动方法中的粗糙微分方程

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-08-07 DOI: 10.1016/j.spa.2025.104757

Ajay Chandra , Léonard Ferdinand

引用次数: 0

Emergence of multivariate extremes in multilayer inhomogeneous random graphs 多层非齐次随机图中多元极值的出现

IF 1.2 2区数学

Stochastic Processes and their Applications Pub Date : 2025-08-06 DOI: 10.1016/j.spa.2025.104762

Daniel Cirkovic , Tiandong Wang , Daren B.H. Cline

{"title":"Emergence of multivariate extremes in multilayer inhomogeneous random graphs","authors":"Daniel Cirkovic , Tiandong Wang , Daren B.H. Cline","doi":"10.1016/j.spa.2025.104762","DOIUrl":"10.1016/j.spa.2025.104762","url":null,"abstract":"<div><div>In this paper we develop a multilayer inhomogeneous random graph model (MIRG). Layers of the MIRG may consist of both single-edge and multi-edge graphs. In the single layer case, it has been shown that the regular variation of the weight distribution underlying the inhomogeneous random graph implies the regular variation of the typical degree distribution. We extend this correspondence to the multilayer case by showing that multivariate regular variation of the weight distribution implies multivariate regular variation of the asymptotic degree distribution. Furthermore, under suitable assumptions, the extremal dependence structure present in the weight distribution will be adopted by the asymptotic degree distribution. By considering the asymptotic degree distribution, a wider class of Chung–Lu and Norros–Reittu graphs may be incorporated into the MIRG layers. Additionally, we prove consistency of the Hill estimator when applied to degrees of the MIRG that have a tail index greater than 1. Simulation results indicate that, in practice, hidden regular variation may be consistently detected from an observed MIRG. Finally, we analyze user interactions on Reddit and observe that they exhibit properties of the MIRG.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104762"},"PeriodicalIF":1.2,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830151","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