Sergey Foss , Dmitry Korshunov , Zbigniew Palmowski
{"title":"Corrigendum to “Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes” [Stochastic Processes and their Applications 176 (2024) 104422]","authors":"Sergey Foss , Dmitry Korshunov , Zbigniew Palmowski","doi":"10.1016/j.spa.2025.104572","DOIUrl":"10.1016/j.spa.2025.104572","url":null,"abstract":"","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104572"},"PeriodicalIF":1.1,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Existence of quasi-stationary distributions for downward skip-free Markov chains","authors":"Kosuke Yamato","doi":"10.1016/j.spa.2025.104579","DOIUrl":"10.1016/j.spa.2025.104579","url":null,"abstract":"<div><div>For downward skip-free continuous-time Markov chains on non-negative integers killed at zero, the existence of the quasi-stationary distribution is studied. The scale function for the process is introduced, and the boundary is classified by a certain integrability condition on the scale function, which gives an extension of Feller’s classification of the boundary for birth-and-death processes. The existence and the set of quasi-stationary distributions are characterized by the scale function and the new classification of the boundary.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104579"},"PeriodicalIF":1.1,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128311","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":"Stability of wandering bumps for Hawkes processes interacting on the circle","authors":"Zoé Agathe-Nerine","doi":"10.1016/j.spa.2025.104577","DOIUrl":"10.1016/j.spa.2025.104577","url":null,"abstract":"<div><div>We consider a population of Hawkes processes modeling the activity of <span><math><mi>N</mi></math></span> interacting neurons. The neurons are regularly positioned on the circle <span><math><mrow><mo>[</mo><mo>−</mo><mi>π</mi><mo>,</mo><mi>π</mi><mo>]</mo></mrow></math></span>, and the connectivity between neurons is given by a cosine kernel. The firing rate function is a sigmoid. The large population limit admits a locally stable manifold of stationary solutions. The main result of the paper concerns the long-time proximity of the synaptic voltage of the population to this manifold in polynomial times in <span><math><mi>N</mi></math></span>. We show in particular that the phase of the voltage along this manifold converges towards a Brownian motion on a time scale of order <span><math><mi>N</mi></math></span>.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104577"},"PeriodicalIF":1.1,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142340","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":"Almost sure limit theorems with applications to non-regular continued fraction algorithms","authors":"Claudio Bonanno , Tanja I. Schindler","doi":"10.1016/j.spa.2025.104573","DOIUrl":"10.1016/j.spa.2025.104573","url":null,"abstract":"<div><div>We consider a conservative ergodic measure-preserving transformation <span><math><mi>T</mi></math></span> of the measure space <span><math><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></math></span> with <span><math><mi>μ</mi></math></span> a <span><math><mi>σ</mi></math></span>-finite measure and <span><math><mrow><mi>μ</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>=</mo><mi>∞</mi></mrow></math></span>. Given an observable <span><math><mrow><mi>g</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>R</mi></mrow></math></span>, it is well known from results by Aaronson, see Aaronson (1997), that in general the asymptotic behaviour of the Birkhoff sums <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>N</mi></mrow></msub><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>:</mo><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>N</mi></mrow></msubsup><mspace></mspace><mrow><mo>(</mo><mi>g</mi><mo>∘</mo><msup><mrow><mi>T</mi></mrow><mrow><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> strongly depends on the point <span><math><mrow><mi>x</mi><mo>∈</mo><mi>X</mi></mrow></math></span>, and that there exists no sequence <span><math><mrow><mo>(</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>)</mo></mrow></math></span> for which <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>N</mi></mrow></msub><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>/</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>→</mo><mn>1</mn></mrow></math></span> for <span><math><mi>μ</mi></math></span>-almost every <span><math><mrow><mi>x</mi><mo>∈</mo><mi>X</mi></mrow></math></span>. In this paper we consider the case <span><math><mrow><mi>g</mi><mo>⁄</mo><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></mrow></math></span> and continue the investigation initiated in Bonanno and Schindler (2022). We show that for transformations <span><math><mi>T</mi></math></span> with strong mixing assumptions for the induced map on a finite measure set, the almost sure asymptotic behaviour of <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>N</mi></mrow></msub><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> for an unbounded observable <span><math><mi>g</mi></math></span> may be obtained using two methods, addition to <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>N</mi></mrow></msub><mi>g</mi></mrow></math></span> of a number of summands depending on <span><math><mi>x</mi></math></span> and trimming. The obtained sums are then asymptotic to a scalar multiple of <span><math><mi>N</mi></math></span>. The results are applied to a couple of non-regular continued fraction algorithms, the backward (or Rényi type) continued fraction and the even-integer c","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104573"},"PeriodicalIF":1.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143139436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The accumulation of beneficial mutations and convergence to a Poisson process","authors":"Nantawat Udomchatpitak, Jason Schweinsberg","doi":"10.1016/j.spa.2025.104578","DOIUrl":"10.1016/j.spa.2025.104578","url":null,"abstract":"<div><div>We consider a model of a population with fixed size <span><math><mi>N</mi></math></span>, which is subjected to an unlimited supply of beneficial mutations at a constant rate <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span>. Individuals with <span><math><mi>k</mi></math></span> beneficial mutations have the fitness <span><math><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>k</mi></mrow></msup></math></span>. Each individual dies at rate 1 and is replaced by a random individual chosen with probability proportional to its fitness. We show that when <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>≪</mo><mn>1</mn><mo>/</mo><mrow><mo>(</mo><mi>N</mi><mo>log</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mi>η</mi></mrow></msup><mo>≪</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>≪</mo><mn>1</mn></mrow></math></span> for some <span><math><mrow><mi>η</mi><mo><</mo><mn>1</mn></mrow></math></span>, the fixation times of beneficial mutations, after a time scaling, converge to the times of a Poisson process, even though for some choices of <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> satisfying these conditions, there will sometimes be multiple beneficial mutations with distinct origins in the population, competing against each other.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104578"},"PeriodicalIF":1.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Almost sure approximations and laws of iterated logarithm for signatures","authors":"Yuri Kifer","doi":"10.1016/j.spa.2025.104576","DOIUrl":"10.1016/j.spa.2025.104576","url":null,"abstract":"<div><div>We obtain strong invariance principles for normalized multiple iterated sums and integrals of the form <span><math><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mi>N</mi></mrow><mrow><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></mrow></msubsup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mi>ν</mi><mo>/</mo><mn>2</mn></mrow></msup><msub><mrow><mo>∑</mo></mrow><mrow><mn>0</mn><mo>≤</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo><</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo><</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>≤</mo><mi>N</mi><mi>t</mi></mrow></msub><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>⊗</mo><mo>⋯</mo><mo>⊗</mo><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>t</mi><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></mrow></math></span> and <span><math><mrow><msubsup><mrow><mi>S</mi></mrow><mrow><mi>N</mi></mrow><mrow><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></mrow></msubsup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mi>ν</mi><mo>/</mo><mn>2</mn></mrow></msup><msub><mrow><mo>∫</mo></mrow><mrow><mn>0</mn><mo>≤</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≤</mo><mo>⋯</mo><mo>≤</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>≤</mo><mi>N</mi><mi>t</mi></mrow></msub><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>⊗</mo><mo>⋯</mo><mo>⊗</mo><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>)</mo></mrow><mi>d</mi><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⋯</mo><mi>d</mi><msub><mrow><mi>s</mi></mrow><mrow><mi>ν</mi></mrow></msub></mrow></math></span>, where <span><math><msub><mrow><mrow><mo>{</mo><mi>ξ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>}</mo></mrow></mrow><mrow><mo>−</mo><mi>∞</mi><mo><</mo><mi>k</mi><mo><</mo><mi>∞</mi></mrow></msub></math></span> and <span><math><msub><mrow><mrow><mo>{</mo><mi>ξ</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>}</mo></mrow></mrow><mrow><mo>−</mo><mi>∞</mi><mo><</mo><mi>s</mi><mo><</mo><mi>∞</mi></mrow></msub></math></span> are centered stationary vector processes with some weak dependence properties. These imply also laws of iterated logarithm and an almost sure central limit theorem for such objects. In the continuous time we work both under direct weak dependence assumptions and also within the suspension setup which is more appropriate for applications in dynamical systems. Similar results under substantially more restricted conditions were obtained in Friz and Kifer (2024) relying heavily on rough paths theory and notations while here we obtain these results in a more direct way","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104576"},"PeriodicalIF":1.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142343","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":"Berry-Esseen bounds for functionals of independent random variables","authors":"Qi-Man Shao , Zhuo-Song Zhang","doi":"10.1016/j.spa.2025.104574","DOIUrl":"10.1016/j.spa.2025.104574","url":null,"abstract":"<div><div>We develop a new Berry–Esseen bound for functionals of independent random variables by introducing a simple form of Chatterjee’s perturbative approach. The main result is applied to the weighted triangle counts in inhomogeneous random graphs, random field Curie–Weiss model, set approximation with random tessellations and random sphere of influence graph models. The rate of convergence is the best possible.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104574"},"PeriodicalIF":1.1,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143139379","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}
Nicholas J.A. Harvey , Christopher Liaw , Victor S. Portella
{"title":"On the expected ℓ∞-norm of high-dimensional martingales","authors":"Nicholas J.A. Harvey , Christopher Liaw , Victor S. Portella","doi":"10.1016/j.spa.2025.104575","DOIUrl":"10.1016/j.spa.2025.104575","url":null,"abstract":"<div><div>Motivated by a problem from theoretical machine learning, we show asymptotically optimal bounds on <span><math><mrow><mo>E</mo><mfenced><mrow><mspace></mspace><msub><mrow><mfenced><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></mfenced></mrow><mrow><mi>∞</mi></mrow></msub><mspace></mspace></mrow></mfenced><mo>/</mo><mo>E</mo><mfenced><mrow><mspace></mspace><msqrt><mrow><mi>τ</mi></mrow></msqrt><mspace></mspace></mrow></mfenced></mrow></math></span>, where <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> is a continuous stochastic process in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi><mo>,</mo><mi>i</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> being a Brownian motion for each <span><math><mrow><mi>i</mi><mo>∈</mo><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></mrow></mrow></math></span> and <span><math><mi>τ</mi></math></span> being a stopping time such that <span><math><mrow><mo>E</mo><mfenced><mrow><mspace></mspace><msqrt><mrow><mi>τ</mi></mrow></msqrt><mspace></mspace></mrow></mfenced><mo><</mo><mi>∞</mi></mrow></math></span>. We further extend this result to the setting where the entries of <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> have smooth quadratic variation. Finally, we show a similar result for discrete-time processes using analogous techniques, together with a discrete version of Itô’s formula.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104575"},"PeriodicalIF":1.1,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138773","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":"Local limit theorem for time-inhomogeneous functions of Markov processes","authors":"Leonid Koralov , Shuo Yan","doi":"10.1016/j.spa.2025.104567","DOIUrl":"10.1016/j.spa.2025.104567","url":null,"abstract":"<div><div>In this paper, we consider a continuous-time Markov process and prove a local limit theorem for the integral of a time-inhomogeneous function of the process. One application is in the study of the fast-oscillating perturbations of linear dynamical systems.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104567"},"PeriodicalIF":1.1,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Raluca M. Balan , Jingyu Huang , Xiong Wang , Panqiu Xia , Wangjun Yuan
{"title":"Gaussian fluctuations for the wave equation under rough random perturbations","authors":"Raluca M. Balan , Jingyu Huang , Xiong Wang , Panqiu Xia , Wangjun Yuan","doi":"10.1016/j.spa.2025.104569","DOIUrl":"10.1016/j.spa.2025.104569","url":null,"abstract":"<div><div>In this article, we consider the stochastic wave equation in spatial dimension <span><math><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></math></span>, with linear term <span><math><mrow><mi>σ</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>u</mi></mrow></math></span> multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with Hurst index <span><math><mrow><mi>H</mi><mo>∈</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mrow></math></span>. First, we prove that the solution is strictly stationary and ergodic in the spatial variable. Then, we show that with proper normalization and centering, the spatial average of the solution converges to the standard normal distribution, and we estimate the rate of this convergence in the total variation distance. We also prove the corresponding functional convergence result.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104569"},"PeriodicalIF":1.1,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
