Stochastic Processes and their Applications最新文献

{"title":"The zero viscosity limit of stochastic Navier–Stokes flows","authors":"Daniel Goodair,&nbsp;Dan Crisan","doi":"10.1016/j.spa.2025.104717","DOIUrl":"10.1016/j.spa.2025.104717","url":null,"abstract":"<div><div>We introduce an analogue to Kato’s Criterion regarding the inviscid convergence of weak solutions of the stochastic Navier–Stokes equations to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type noise models. This is achieved firstly for the typical noise scaling of <span><math><msup><mrow><mi>ν</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></math></span>, before considering a new parameter which approaches zero with viscosity but at a potentially different rate. We determine the implications of this for our criterion and clarify a sense in which the scaling by <span><math><msup><mrow><mi>ν</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></math></span> is optimal. The criterion applies in both two and three dimensions, with some technical simplifications in the 2D case.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104717"},"PeriodicalIF":1.1,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366774","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}

{"title":"Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in C1,β open sets","authors":"Renming Song ,&nbsp;Peixue Wu ,&nbsp;Shukun Wu","doi":"10.1016/j.spa.2025.104727","DOIUrl":"10.1016/j.spa.2025.104727","url":null,"abstract":"<div><div>Let <span><math><mi>D</mi></math></span> be an open set of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> and let <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>D</mi></mrow></msubsup></math></span> be the generator of the censored <span><math><mi>α</mi></math></span>-stable process in <span><math><mi>D</mi></math></span>. In this paper, we establish sharp two-sided heat kernel estimates for <span><math><mrow><msubsup><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>D</mi></mrow></msubsup><mo>−</mo><mi>κ</mi></mrow></math></span>, with <span><math><mi>κ</mi></math></span> being a non-negative critical potential and <span><math><mi>D</mi></math></span> being a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>β</mi></mrow></msup></math></span> open set, <span><math><mrow><mi>β</mi><mo>∈</mo><mrow><mo>(</mo><msub><mrow><mrow><mo>(</mo><mi>α</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mo>+</mo></mrow></msub><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span>. The potential <span><math><mi>κ</mi></math></span> can exhibit multi-singularities and our regularity assumption on <span><math><mi>D</mi></math></span> is weaker than the regularity assumed in earlier literature on heat kernel estimates of fractional Laplacians.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104727"},"PeriodicalIF":1.1,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322960","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}

{"title":"New continuity results for a class of time fractional stochastic heat equations in bounded and unbounded domains","authors":"Nguyen Huy Tuan ,&nbsp;Erkan Nane","doi":"10.1016/j.spa.2025.104687","DOIUrl":"10.1016/j.spa.2025.104687","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we consider a class of time fractional stochastic heat type equation &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̇&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is the Caputo fractional derivative, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is a Lipschitz continuous function, and &lt;span&gt;&lt;math&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̇&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/math&gt;&lt;/span&gt; is space–time white noise. These equations have significant applications in modeling temperature in thermal materials. Our main purpose in this paper is to study the continuity of solutions of fractional order Equation (1) with respect to &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. Two interesting questions for our problem are stated as follows. Let &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; be the solution of Equation (1) for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, respectively. The first question is that : Does &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; in an appropriate sense as &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;? The second question is that: Does &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; in an appropriate sense as &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;? We will give affirmative answers to both of these questions. Furthermore, under some suitable assumptions on the initial datum, we provide the convergence rate estimates between &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/m","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104687"},"PeriodicalIF":1.1,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306824","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}

{"title":"Convergence rates for Chernoff-type approximations of convex monotone semigroups","authors":"Jonas Blessing ,&nbsp;Lianzi Jiang ,&nbsp;Michael Kupper ,&nbsp;Gechun Liang","doi":"10.1016/j.spa.2025.104700","DOIUrl":"10.1016/j.spa.2025.104700","url":null,"abstract":"<div><div>We provide explicit convergence rates for Chernoff-type approximations of convex monotone semigroups which have the form <span><math><mrow><mi>S</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>f</mi><mo>=</mo><msub><mrow><mo>lim</mo></mrow><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></msub><mi>I</mi><msup><mrow><mrow><mo>(</mo><mfrac><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></mfrac><mo>)</mo></mrow></mrow><mrow><mi>n</mi></mrow></msup><mi>f</mi></mrow></math></span> for bounded continuous functions <span><math><mi>f</mi></math></span>. Under suitable conditions on the one-step operators <span><math><mrow><mi>I</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> regarding the time regularity and consistency of the approximation scheme, we obtain <span><math><mrow><msub><mrow><mo>‖</mo><mi>S</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>f</mi><mo>−</mo><mi>I</mi><msup><mrow><mrow><mo>(</mo><mfrac><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></mfrac><mo>)</mo></mrow></mrow><mrow><mi>n</mi></mrow></msup><mi>f</mi><mo>‖</mo></mrow><mrow><mi>∞</mi></mrow></msub><mo>≤</mo><mi>c</mi><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mi>γ</mi></mrow></msup></mrow></math></span> for bounded Lipschitz continuous functions <span><math><mi>f</mi></math></span>, where <span><math><mrow><mi>c</mi><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>γ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> are determined explicitly. Moreover, the mapping <span><math><mrow><mi>t</mi><mo>↦</mo><mi>S</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>f</mi></mrow></math></span> is Hölder continuous. These results are closely related to monotone approximation schemes for viscosity solutions but are obtained independently by following a recently developed semigroup approach to Hamilton–Jacobi–Bellman equations which uniquely characterizes semigroups via their <span><math><mi>Γ</mi></math></span>-generators. The different approach allows to consider convex rather than sublinear equations and the results can be extended to unbounded functions by modifying the norm with a suitable weight function. Furthermore, up to possibly different consistency errors for the operators <span><math><mrow><mi>I</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, the upper and lower bound for the error between the semigroup and the iterated operators are symmetric. The abstract results are applied to Nisio semigroups and limit theorems for convex expectations.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104700"},"PeriodicalIF":1.1,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144288806","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}

{"title":"Spectral bounds for exit times on metric measure Dirichlet spaces and applications","authors":"Phanuel Mariano ,&nbsp;Jing Wang","doi":"10.1016/j.spa.2025.104707","DOIUrl":"10.1016/j.spa.2025.104707","url":null,"abstract":"<div><div>Assuming the heat kernel on a doubling Dirichlet metric measure space has a sub-Gaussian bound, we prove an asymptotically sharp spectral upper bound on the survival probability of the associated diffusion process. As a consequence, we can show that the supremum of the mean exit time over all starting points is finite if and only if the bottom of the spectrum is positive. Among several applications, we show that the spectral upper bound on the survival probability implies a bound for the Hot Spots constant for Riemannian manifolds. Our results apply to interesting geometric settings including sub-Riemannian manifolds and fractals.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104707"},"PeriodicalIF":1.1,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322808","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}

{"title":"Discrete time optimal investment under model uncertainty","authors":"Laurence Carassus ,&nbsp;Massinissa Ferhoune","doi":"10.1016/j.spa.2025.104708","DOIUrl":"10.1016/j.spa.2025.104708","url":null,"abstract":"<div><div>We study a robust utility maximisation problem in a general discrete-time frictionless market under quasi-sure no-arbitrage. The investor is assumed to have a random and concave utility function defined on the whole real line. She also faces model ambiguity in her beliefs about the market, which is modelled through a set of priors. We prove the existence of an optimal investment strategy using only primal methods. For that, we assume classical assumptions on the market and the random utility function as asymptotic elasticity constraints. Most of our other assumptions are stated on a prior-by-prior basis and correspond to generally accepted assumptions in the literature on markets without ambiguity. We also propose a general setting, including utility functions with benchmarks for which our assumptions can be easily checked.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104708"},"PeriodicalIF":1.1,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291409","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}

{"title":"Planar reinforced k-out percolation","authors":"Gideon Amir ,&nbsp;Markus Heydenreich ,&nbsp;Christian Hirsch","doi":"10.1016/j.spa.2025.104706","DOIUrl":"10.1016/j.spa.2025.104706","url":null,"abstract":"<div><div>We investigate the percolation properties of a planar reinforced network model. In this model, at every time step, every vertex chooses <span><math><mrow><mi>k</mi><mo>⩾</mo><mn>1</mn></mrow></math></span> incident edges, whose weight is then increased by 1. The choice of this <span><math><mi>k</mi></math></span>-tuple occurs proportionally to the product of the corresponding edge weights raised to some power <span><math><mrow><mi>α</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>.</div><div>Our investigations are guided by the conjecture that the set of infinitely reinforced edges percolates for <span><math><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>α</mi><mo>≫</mo><mn>1</mn></mrow></math></span>. First, we study the case <span><math><mrow><mi>α</mi><mo>=</mo><mi>∞</mi></mrow></math></span>, where we show the percolation for <span><math><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow></math></span> after adding arbitrarily sparse independent sprinkling and also allowing dual connectivities. We also derive a finite-size criterion for percolation without sprinkling. Then, we extend this finite-size criterion to the <span><math><mrow><mi>α</mi><mo>&lt;</mo><mi>∞</mi></mrow></math></span> case. Finally, we verify these conditions numerically.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104706"},"PeriodicalIF":1.1,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241427","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}

{"title":"Percolation with random one-dimensional reinforcements","authors":"A. Nascimento ,&nbsp;R. Sanchis ,&nbsp;D. Ungaretti","doi":"10.1016/j.spa.2025.104704","DOIUrl":"10.1016/j.spa.2025.104704","url":null,"abstract":"<div><div>We study inhomogeneous Bernoulli bond percolation on the graph <span><math><mrow><mi>G</mi><mo>×</mo><mi>Z</mi></mrow></math></span>, where <span><math><mi>G</mi></math></span> is a connected quasi-transitive graph. The inhomogeneity is introduced through a random region <span><math><mi>R</mi></math></span> around the <em>origin axis</em> <span><math><mrow><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow><mo>×</mo><mi>Z</mi></mrow></math></span>, where each edge in <span><math><mi>R</mi></math></span> is open with probability <span><math><mi>q</mi></math></span> and all other edges are open with probability <span><math><mi>p</mi></math></span>. When the region <span><math><mi>R</mi></math></span> is defined by stacking or overlapping boxes with random radii centered along the origin axis, we derive conditions on the moments of the radii, based on the growth properties of <span><math><mi>G</mi></math></span>, so that for any subcritical <span><math><mi>p</mi></math></span> and any <span><math><mrow><mi>q</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>, the non-percolative phase persists.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104704"},"PeriodicalIF":1.1,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194425","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}

{"title":"Sequential common change detection, isolation, and estimation in multiple compound Poisson processes","authors":"Dong-Yun Kim,&nbsp;Wei Biao Wu,&nbsp;Yanhong Wu","doi":"10.1016/j.spa.2025.104701","DOIUrl":"10.1016/j.spa.2025.104701","url":null,"abstract":"<div><div>We explore and compare the detection of changes in both the arrival rate and jump size mean and estimation of change-time after detection within a compound Poisson process by using generalized CUSUM and Shiryayev–Roberts (S–R) procedures. Average in-control and out-of control lengths are derived as well as the limiting distribution of the generalized CUSUM processes. The asymptotic bias of change time estimation is also derived. To detect a common change in multiple compound Poisson processes where change only occurs in a portion of panels, a unified algorithm is proposed that employs the sum of S–R processes to detect a common change, uses individual CUSUM processes to isolate the changed panels with False Discovery Rate (FDR) control, and then estimate the common change time as the median of the estimates obtained from the isolated channels. To illustrate the approach, we apply it to mining disaster data in the USA.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104701"},"PeriodicalIF":1.1,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144190340","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}

{"title":"Majority dynamics on random graphs: The multiple states case","authors":"Jordan Chellig,&nbsp;Nikolaos Fountoulakis","doi":"10.1016/j.spa.2025.104682","DOIUrl":"10.1016/j.spa.2025.104682","url":null,"abstract":"<div><div>We study the evolution of majority dynamics with more than two states on the binomial random graph <span><math><mrow><mi>G</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>p</mi><mo>)</mo></mrow></mrow></math></span>. In this process, each vertex has a state in <span><math><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>}</mo></mrow></math></span>, with <span><math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, and at each round every vertex adopts state <span><math><mi>i</mi></math></span> if it has more neighbours in state <span><math><mi>i</mi></math></span> than in any other state. Ties are resolved randomly. We show that with high probability the process reaches unanimity in at most three rounds, if <span><math><mrow><mi>n</mi><mi>p</mi><mo>≫</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104682"},"PeriodicalIF":1.1,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203837","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}