Stochastic Processes and their Applications最新文献

{"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}

{"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}

{"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}

{"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}

{"title":"On decomposition of the last passage time of diffusions","authors":"Masahiko Egami,&nbsp;Rusudan Kevkhishvili","doi":"10.1016/j.spa.2025.104563","DOIUrl":"10.1016/j.spa.2025.104563","url":null,"abstract":"<div><div>For a regular transient diffusion, we derive the decomposition formula of the Laplace transform of the last passage time to a certain state <span><math><mi>α</mi></math></span> explicitly in a simple form in terms of the Green functions, which also leads to the Green function’s decomposition formula. This is accomplished by transforming the original diffusion into two diffusions using the occupation time of the area above and below <span><math><mi>α</mi></math></span>. We demonstrate applications of the decomposition formulas to various diffusions including a Brownian motion with two-valued drift and present a financial example of the leverage effect caused by the stock price with switching volatility.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104563"},"PeriodicalIF":1.1,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142653","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":"Hopfield neural lattice models with locally Lipschitz coefficients driven by Lévy noise","authors":"Renhai Wang ,&nbsp;Hailang Bai ,&nbsp;Pengyu Chen ,&nbsp;Mirelson M. Freitas","doi":"10.1016/j.spa.2024.104559","DOIUrl":"10.1016/j.spa.2024.104559","url":null,"abstract":"<div><div>In this article, we study the global-in-time solvability and long-term dynamics of a wide class of infinite-dimensional Hopfield neural models on <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> of infinitely many ODEs with a family of locally Lipschitz coefficients driven by Lévy noise. There are three new features of this stochastic model: (1)The Lévy noise is characterized by two sequence of mutually independent <em>two-sided</em> (including negative initial times) Wiener processes and Poisson random measures; (2)The diffusion coefficients of the Lévy noise are locally Lipschitz associated with an appropriate weight; (3)The connection strength <span><math><msub><mrow><mi>ξ</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></math></span> between the <span><math><mi>i</mi></math></span>th and <span><math><mi>j</mi></math></span>th neurons has a finite reciprocal-weighted aggregate efficacy in a weak sense. This Lévy noise driven lattice equation is formulated as an abstract one in an infinite-dimensional weighted Hilbert space <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mi>ϱ</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span>. Both global-in-time well-posedness and long-time dynamics of this abstract stochastic system are investigated under certain conditions. In particular, we show that the long-time dynamics of the stochastic systems can be captured by a weakly compact and weakly attracting mean random attractor in the Bochner space <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mover><mrow><mi>Ω</mi></mrow><mrow><mo>̃</mo></mrow></mover><mo>,</mo><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mi>ϱ</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow></mrow></math></span> over a complete filtered probability space <span><math><mrow><mo>(</mo><mover><mrow><mi>Ω</mi></mrow><mrow><mo>̃</mo></mrow></mover><mo>,</mo><mover><mrow><mi>F</mi></mrow><mrow><mo>̃</mo></mrow></mover><mo>,</mo><msub><mrow><mrow><mo>{</mo><msub><mrow><mover><mrow><mi>F</mi></mrow><mrow><mo>̃</mo></mrow></mover></mrow><mrow><mi>t</mi></mrow></msub><mo>}</mo></mrow></mrow><mrow><mi>t</mi><mo>∈</mo><mi>R</mi></mrow></msub><mo>,</mo><mi>P</mi><mo>)</mo></mrow></math></span>. It seems that this is the first time to study the well-posedness and dynamics of lattice Hopfield neural models with locally Lipschitz coefficients driven by Lévy noise even in the autonomous case.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"181 ","pages":"Article 104559"},"PeriodicalIF":1.1,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143101900","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":"Convex integral functionals of càdlàg processes","authors":"Ari-Pekka Perkkiö ,&nbsp;Erick Treviño-Aguilar","doi":"10.1016/j.spa.2024.104561","DOIUrl":"10.1016/j.spa.2024.104561","url":null,"abstract":"<div><div>This article characterizes conjugates and subdifferentials of convex integral functionals over linear spaces of <span><math><mtext>càdlàg</mtext></math></span> stochastic processes. The approach is based on new measurability results on the Skorokhod space and new interchange rules of integral functionals that are developed in the article. The main results provide a general approach to apply convex duality in a variety of optimization problems ranging from optimal stopping to singular stochastic control and mathematical finance.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"181 ","pages":"Article 104561"},"PeriodicalIF":1.1,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143101901","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":"On local maxima of smooth Gaussian nonstationary processes and stationary planar fields with trends","authors":"Dan Cheng","doi":"10.1016/j.spa.2024.104560","DOIUrl":"10.1016/j.spa.2024.104560","url":null,"abstract":"<div><div>We present exact formulas for both the expected number and the height distribution of local maxima (peaks) in two distinct categories of smooth, non-centered Gaussian fields: (i) nonstationary Gaussian processes and (ii) stationary planar Gaussian fields. For case (i), we introduce a novel parameter related to conditional correlation that significantly simplifies the computation of these formulas. Notably, the peak height distribution is solely dependent on this single parameter. In case (ii), traditional methods involving GOE random matrices are ineffective for non-isotropic fields with mean functions. To address this, we apply specific transformations that enable the derivation of formulas using generalized chi-squared density functions. These derived results provide essential tools for calculating p-values and power in applications of signal and change point detection within environments characterized by non-isotropic Gaussian noise.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"181 ","pages":"Article 104560"},"PeriodicalIF":1.1,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128608","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":"Filtered data based estimators for stochastic processes driven by colored noise","authors":"Grigorios A. Pavliotis ,&nbsp;Sebastian Reich ,&nbsp;Andrea Zanoni","doi":"10.1016/j.spa.2024.104558","DOIUrl":"10.1016/j.spa.2024.104558","url":null,"abstract":"<div><div>We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer parameters in the limit equation, driven by white noise, given observations of the colored noise dynamics. We consider both the maximum likelihood and the stochastic gradient descent in continuous time estimators, and we propose to modify them by including filtered data. We provide a convergence analysis for our estimators showing their asymptotic unbiasedness in a general setting and asymptotic normality under a simplified scenario.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"181 ","pages":"Article 104558"},"PeriodicalIF":1.1,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128606","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":"Evolving privacy: Drift parameter estimation for discretely observed i.i.d. diffusion processes under LDP","authors":"Chiara Amorino ,&nbsp;Arnaud Gloter ,&nbsp;Hélène Halconruy","doi":"10.1016/j.spa.2024.104557","DOIUrl":"10.1016/j.spa.2024.104557","url":null,"abstract":"<div><div>The problem of estimating a parameter in the drift coefficient is addressed for <span><math><mi>N</mi></math></span> discretely observed independent and identically distributed stochastic differential equations (SDEs). This is done considering additional constraints, wherein only public data can be published and used for inference. The concept of local differential privacy (LDP) is formally introduced for a system of stochastic differential equations. The objective is to estimate the drift parameter by proposing a contrast function based on a pseudo-likelihood approach. A suitably scaled Laplace noise is incorporated to meet the privacy requirements. Our key findings encompass the derivation of explicit conditions tied to the privacy level. Under these conditions, we establish the consistency and asymptotic normality of the associated estimator. Notably, the convergence rate is intricately linked to the privacy level, and in some situations may be completely different from the case where privacy constraints are ignored. Our results hold true as the discretization step approaches zero and the number of processes <span><math><mi>N</mi></math></span> tends to infinity.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"181 ","pages":"Article 104557"},"PeriodicalIF":1.1,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143127948","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}