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Stochastic Processes and their Applications最新文献

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On the expected ℓ∞-norm of high-dimensional martingales
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-01-18 DOI: 10.1016/j.spa.2025.104575
Nicholas J.A. Harvey , Christopher Liaw , Victor S. Portella
{"title":"On the expected ℓ∞-norm of high-dimensional martingales","authors":"Nicholas J.A. Harvey ,&nbsp;Christopher Liaw ,&nbsp;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>&lt;</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}
引用次数: 0
Local limit theorem for time-inhomogeneous functions of Markov processes
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-01-16 DOI: 10.1016/j.spa.2025.104567
Leonid Koralov , Shuo Yan
{"title":"Local limit theorem for time-inhomogeneous functions of Markov processes","authors":"Leonid Koralov ,&nbsp;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}
引用次数: 0
Gaussian fluctuations for the wave equation under rough random perturbations
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-01-16 DOI: 10.1016/j.spa.2025.104569
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 ,&nbsp;Jingyu Huang ,&nbsp;Xiong Wang ,&nbsp;Panqiu Xia ,&nbsp;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}
引用次数: 0
The compact support property of rough super Brownian motion on R2
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-01-15 DOI: 10.1016/j.spa.2025.104568
Ruhong Jin , Nicolas Perkowski
{"title":"The compact support property of rough super Brownian motion on R2","authors":"Ruhong Jin ,&nbsp;Nicolas Perkowski","doi":"10.1016/j.spa.2025.104568","DOIUrl":"10.1016/j.spa.2025.104568","url":null,"abstract":"<div><div>We discuss the compact support property of the rough super-Brownian motion constructed in Perkowski and Rosati (2021) as a scaling limit of a branching random walk in static random environment. The semi-linear equation corresponding to this measure-valued process is the continuous parabolic Anderson model, a singular SPDE in need of renormalization, which prevents the use of classical PDE arguments as in Englander (2006). But with the help of an interior estimation method developed in Moinat (2020), we are able to show that the compact support property also holds for rough super-Brownian motion.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104568"},"PeriodicalIF":1.1,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142337","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}
引用次数: 0
Strong approximations in the almost sure central limit theorem and limit behavior of the center of mass
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-01-15 DOI: 10.1016/j.spa.2025.104570
Zhishui Hu , Wei Wang , Liang Dong
{"title":"Strong approximations in the almost sure central limit theorem and limit behavior of the center of mass","authors":"Zhishui Hu ,&nbsp;Wei Wang ,&nbsp;Liang Dong","doi":"10.1016/j.spa.2025.104570","DOIUrl":"10.1016/j.spa.2025.104570","url":null,"abstract":"<div><div>In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a random sequence under a different strong approximation condition. Applications to step-reinforced random walks are also discussed.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104570"},"PeriodicalIF":1.1,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142347","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
Exact asymptotics of ruin probabilities with linear Hawkes arrivals
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-01-14 DOI: 10.1016/j.spa.2025.104571
Zbigniew Palmowski , Simon Pojer , Stefan Thonhauser
{"title":"Exact asymptotics of ruin probabilities with linear Hawkes arrivals","authors":"Zbigniew Palmowski ,&nbsp;Simon Pojer ,&nbsp;Stefan Thonhauser","doi":"10.1016/j.spa.2025.104571","DOIUrl":"10.1016/j.spa.2025.104571","url":null,"abstract":"<div><div>In this contribution we consider a risk process whose arrivals are driven by a linear marked Hawkes process. Using an appropriate change of measure and a generalized renewal theorem, we are able to derive the exact asymptotics of the process’s ruin probability in the case of light-tailed claims. On the other hand, we can exploit the principle of one large jump to derive the analogous result in the heavy-tailed situation. Furthermore, we derive several intermediate results like the Harris recurrence of the Hawkes intensity process which are of their own interest.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104571"},"PeriodicalIF":1.1,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142339","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
Local weak limits for collapsed branching processes with random out-degrees
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-01-11 DOI: 10.1016/j.spa.2025.104566
Sayan Banerjee, Prabhanka Deka, Mariana Olvera-Cravioto
{"title":"Local weak limits for collapsed branching processes with random out-degrees","authors":"Sayan Banerjee,&nbsp;Prabhanka Deka,&nbsp;Mariana Olvera-Cravioto","doi":"10.1016/j.spa.2025.104566","DOIUrl":"10.1016/j.spa.2025.104566","url":null,"abstract":"<div><div>We obtain local weak limits in probability for Collapsed Branching Processes (CBP), which are directed random networks obtained by collapsing random-sized families of individuals in a general continuous-time branching process. The local weak limit of a given CBP, as the network grows, is shown to be a related continuous-time branching process stopped at an independent exponential time. The proof involves the construction of an explicit coupling of the in-components of vertices with the limiting object. We also show that the in-components of a finite collection of uniformly chosen vertices locally weakly converge (in probability) to i.i.d. copies of the above limit, reminiscent of propagation of chaos in interacting particle systems. We obtain as special cases novel descriptions of the local weak limits of directed preferential and uniform attachment models. We also outline some applications of our results for analyzing the limiting in-degree and PageRank distributions. In particular, upper and lower bounds on the tail of the in-degree distribution are obtained and a phase transition is detected in terms of the growth rate of the attachment function governing reproduction rates in the branching process.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104566"},"PeriodicalIF":1.1,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142338","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 the site frequency spectrum of neutral mutations in an exponentially growing population
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-01-11 DOI: 10.1016/j.spa.2025.104565
Einar Bjarki Gunnarsson , Kevin Leder , Xuanming Zhang
{"title":"Limit theorems for the site frequency spectrum of neutral mutations in an exponentially growing population","authors":"Einar Bjarki Gunnarsson ,&nbsp;Kevin Leder ,&nbsp;Xuanming Zhang","doi":"10.1016/j.spa.2025.104565","DOIUrl":"10.1016/j.spa.2025.104565","url":null,"abstract":"<div><div>The site frequency spectrum (SFS) is a widely used summary statistic of genomic data. Motivated by recent evidence for the role of neutral evolution in cancer, we investigate the SFS of neutral mutations in an exponentially growing population. Using branching process techniques, we establish (first-order) almost sure convergence results for the SFS of a Galton–Watson process, evaluated either at a fixed time or at the stochastic time at which the population first reaches a certain size. We finally use our results to construct consistent estimators for the extinction probability and the effective mutation rate of a birth–death process.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104565"},"PeriodicalIF":1.1,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142341","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
McKean–Vlasov stochastic equations with Hölder coefficients
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-01-09 DOI: 10.1016/j.spa.2025.104564
Andrea Pascucci, Alessio Rondelli
{"title":"McKean–Vlasov stochastic equations with Hölder coefficients","authors":"Andrea Pascucci,&nbsp;Alessio Rondelli","doi":"10.1016/j.spa.2025.104564","DOIUrl":"10.1016/j.spa.2025.104564","url":null,"abstract":"<div><div>This work revisits the well-posedness of non-degenerate McKean–Vlasov stochastic differential equations with Hölder continuous coefficients, recently established by Chaudru de Raynal. We provide a streamlined and direct proof that leverages standard Gaussian estimates for uniformly parabolic PDEs, bypassing the need for derivatives with respect to the measure argument and extending applicability to hypoelliptic PDEs under weaker assumptions.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104564"},"PeriodicalIF":1.1,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142345","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}
引用次数: 0
Aging and sub-aging for one-dimensional random walks amongst random conductances
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-01-09 DOI: 10.1016/j.spa.2025.104562
D.A. Croydon , D. Kious , C. Scali
{"title":"Aging and sub-aging for one-dimensional random walks amongst random conductances","authors":"D.A. Croydon ,&nbsp;D. Kious ,&nbsp;C. Scali","doi":"10.1016/j.spa.2025.104562","DOIUrl":"10.1016/j.spa.2025.104562","url":null,"abstract":"<div><div>We consider random walks amongst random conductances in the cases where the conductances can be arbitrarily small, with a heavy-tailed distribution at 0, and where the conductances may or may not have a heavy-tailed distribution at infinity. We study the long time behaviour of these processes and prove aging statements. When the heavy tail is only at 0, we prove that aging can be observed for the maximum of the process, i.e. the same maximal value is attained repeatedly over long time-scales. When there are also heavy tails at infinity, we prove a classical aging result for the position of the walker, as well as a sub-aging result that occurs on a shorter time-scale.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104562"},"PeriodicalIF":1.1,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142346","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}
引用次数: 0
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