发布求助
文献互助 智能选刊 最新文献

Annals of Applied Probability最新文献

筛选
英文 中文
Pathwise McKean–Vlasov theory with additive noise 具有加性噪声的路径McKean-Vlasov理论
IF 1.8 2区 数学
Annals of Applied Probability Pub Date : 2020-10-01 DOI: 10.1214/20-AAP1560
M. Coghi, J. Deuschel, P. Friz, M. Maurelli
{"title":"Pathwise McKean–Vlasov theory with additive noise","authors":"M. Coghi, J. Deuschel, P. Friz, M. Maurelli","doi":"10.1214/20-AAP1560","DOIUrl":"https://doi.org/10.1214/20-AAP1560","url":null,"abstract":"We take a pathwise approach to classical McKean-Vlasov stochastic differential equations with additive noise, as e.g. exposed in Sznitmann [38]. Our study was prompted by some concrete problems in battery modelling [23], and also by recent progrss on rough-pathwise McKean-Vlasov theory, notably Cass–Lyons [10], and then Bailleul, Catellier and Delarue [4]. Such a “pathwise McKean-Vlasov theory” can be traced back to Tanaka [40]. This paper can be seen as an attempt to advertize the ideas, power and simplicity of the pathwise appproach, not so easily extracted from [4, 10, 40], together with a number of novel applications. These include mean field convergence without a priori independence and exchangeability assumption; common noise, càdlàg noise, and reflecting boundaries. Last not least, we generalize Dawson–Gärtner large deviations and the central limit theorem to a non-Brownian noise setting.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":"107 1","pages":"2355-2392"},"PeriodicalIF":1.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74759561","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: 24
Deposition, diffusion, and nucleation on an interval 间隔上的沉积、扩散和成核
IF 1.8 2区 数学
Annals of Applied Probability Pub Date : 2020-10-01 DOI: 10.1214/22-AAP1804
Nicholas Georgiou, A. Wade
{"title":"Deposition, diffusion, and nucleation on an interval","authors":"Nicholas Georgiou, A. Wade","doi":"10.1214/22-AAP1804","DOIUrl":"https://doi.org/10.1214/22-AAP1804","url":null,"abstract":"Motivated by nanoscale growth of ultra-thin films, we study a model of deposition, on an interval substrate, of particles that perform Brownian motions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier to subsequent particles. This is a continuum version of a lattice model popular in the applied literature. We show that the associated interval-splitting process converges in the sparse deposition limit to a Markovian process (in the vein of Brennan and Durrett) governed by a splitting density with a compact Fourier series expansion but, apparently, no simple closed form. We show that the same splitting density governs the fixed deposition rate, large time asymptotics of the normalized gap distribution, so these asymptotics are independent of deposition rate. The splitting density is derived by solving an exit problem for planar Brownian motion from a right-angled triangle, extending work of Smith and Watson.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46782945","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
Stochastic approximation on noncompact measure spaces and application to measure-valued Pólya processes 非紧测度空间的随机逼近及其在测度值Pólya过程中的应用
IF 1.8 2区 数学
Annals of Applied Probability Pub Date : 2020-10-01 DOI: 10.1214/20-AAP1561
Cécile Mailler, D. Villemonais
{"title":"Stochastic approximation on noncompact measure spaces and application to measure-valued Pólya processes","authors":"Cécile Mailler, D. Villemonais","doi":"10.1214/20-AAP1561","DOIUrl":"https://doi.org/10.1214/20-AAP1561","url":null,"abstract":"Our main result is to prove almost-sure convergence of a stochastic-approximation algorithm defined on the space of measures on a non-compact space. Our motivation is to apply this result to measure-valued P'olya processes (MVPPs, also known as infinitely-many P'olya urns). Our main idea is to use Foster-Lyapunov type criteria in a novel way to generalize stochastic-approximation methods to measure-valued Markov processes with a non-compact underlying space, overcoming in a fairly general context one of the major difficulties of existing studies on this subject. From the MVPPs point of view, our result implies almost-sure convergence of a large class of MVPPs, this convergence was only obtained until now for specific examples, with only convergence in probability established for general classes. Furthermore, our approach allows us to extend the definition of MVPPs by adding \"weights\" to the different colors of the infinitely-many-color urn. We also exhibit a link between non-\"balanced\" MVPPs and quasi-stationary distributions of Markovian processes, which allows us to treat, for the first time in the literature, the non-balanced case. Finally, we show how our result can be applied to designing stochastic-approximation algorithms for the approximation of quasi-stationary distributions of discrete- and continuous-time Markov processes on non-compact spaces.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":"2010 1","pages":"2393-2438"},"PeriodicalIF":1.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86304936","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: 7
On the minimal drift for recurrence in the frog model on d-ary trees 关于d-ary树上frog模型递推的最小漂移
IF 1.8 2区 数学
Annals of Applied Probability Pub Date : 2020-08-20 DOI: 10.1214/21-aap1755
Chengkun Guo, Si Tang, Ning-Liu Wei
{"title":"On the minimal drift for recurrence in the frog model on d-ary trees","authors":"Chengkun Guo, Si Tang, Ning-Liu Wei","doi":"10.1214/21-aap1755","DOIUrl":"https://doi.org/10.1214/21-aap1755","url":null,"abstract":"We study the recurrence of one-per-site frog model $text{FM}(d, p)$ on a $d$-ary tree with drift parameter $pin [0,1]$, which determines the bias of frogs' random walks. We are interested in the minimal drift $p_{d}$ so that the frog model is recurrent. Using a coupling argument together with a generating function technique, we prove that for all $d ge 2$, $p_{d}le 1/3$, which is the optimal universal upper bound.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46796929","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: 3
Large deviations of mean-field interacting particle systems in a fast varying environment 快速变化环境中平均场相互作用粒子系统的大偏差
IF 1.8 2区 数学
Annals of Applied Probability Pub Date : 2020-08-16 DOI: 10.1214/21-aap1718
S. Yasodharan, R. Sundaresan
{"title":"Large deviations of mean-field interacting particle systems in a fast varying environment","authors":"S. Yasodharan, R. Sundaresan","doi":"10.1214/21-aap1718","DOIUrl":"https://doi.org/10.1214/21-aap1718","url":null,"abstract":"This paper studies large deviations of a \"fully coupled\" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment evolves in the fast time scale. Our main result is the path-space large deviation principle for the joint law of the empirical measure process of the particles and the occupation measure process of the fast environment. This extends previous results known for two time scale diffusions to two time scale mean-field models with jumps. Our proof is based on the method of stochastic exponentials. We characterise the rate function by studying a certain variational problem associated with an exponential martingale.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47768208","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: 2
Growth of stationary Hastings–Levitov 静止黑斯廷斯的增长——Levitov
IF 1.8 2区 数学
Annals of Applied Probability Pub Date : 2020-08-13 DOI: 10.1214/21-AAP1761
Noam Berger, Eviatar B. Procaccia, Amanda G. Turner
{"title":"Growth of stationary Hastings–Levitov","authors":"Noam Berger, Eviatar B. Procaccia, Amanda G. Turner","doi":"10.1214/21-AAP1761","DOIUrl":"https://doi.org/10.1214/21-AAP1761","url":null,"abstract":"We construct and study a stationary version of the Hastings-Levitov$(0)$ model. We prove that, unlike in the classical HL$(0)$ model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL$(0)$ is proposed as a potential candidate for a stationary off-lattice variant of Diffusion Limited Aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finiteness of arms and arm size distribution. We show that, under appropriate scaling, arms in SHL$(0)$ converge to the graph of Brownian motion which has fractal dimension $3/2$. Moreover we show that trees with $n$ particles reach a height of order $n^{2/3}$, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46184941","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: 5
Darwinian evolution as Brownian motion on the simplex: A geometric perspective on stochastic replicator dynamics 作为单纯形上布朗运动的达尔文进化论：随机复制动力学的几何视角
IF 1.8 2区 数学
Annals of Applied Probability Pub Date : 2020-08-12 DOI: 10.1214/22-aap1817
Tobias Lehmann
{"title":"Darwinian evolution as Brownian motion on the simplex: A geometric perspective on stochastic replicator dynamics","authors":"Tobias Lehmann","doi":"10.1214/22-aap1817","DOIUrl":"https://doi.org/10.1214/22-aap1817","url":null,"abstract":"We prove that stochastic replicator dynamics can be interpreted as intrinsic Brownian motion on the simplex equipped the Aitchison geometry. As an immediate consequence we derive three approximation results in the spirit of Wong-Zakai approximation, Donsker's invariance principle and a JKO-scheme. Finally, using the Fokker-Planck equation and Wasserstein-contraction estimates, we study the long time behavior of the stochastic replicator equation, as an example of a non-gradient drift diffusion on the Aitchison simplex.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49035267","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: 1
Regularization of multiplicative SDEs through additive noise 通过加性噪声的乘性SDEs正则化
IF 1.8 2区 数学
Annals of Applied Probability Pub Date : 2020-08-05 DOI: 10.1214/21-aap1778
L. Galeati, Fabian A. Harang
{"title":"Regularization of multiplicative SDEs through additive noise","authors":"L. Galeati, Fabian A. Harang","doi":"10.1214/21-aap1778","DOIUrl":"https://doi.org/10.1214/21-aap1778","url":null,"abstract":"We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to ensure existence and uniqueness of the SDE. We show that suitable perturbations restore existence, uniqueness and regularity of the flow for the resulting equation, even when both the drift and the diffusion coefficients are distributional, thus extending the program of regularization by noise to the case of multiplicative SDEs. \u0000Our method relies on a combination of the non-linear Young formalism developed by Catellier and Gubinelli, and stochastic averaging estimates recently obtained by Hairer and Li.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44448551","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: 15
Invariance principles for integrated random walks conditioned to stay positive 条件保持为正的集成随机漫步的不变性原则
IF 1.8 2区 数学
Annals of Applied Probability Pub Date : 2020-07-26 DOI: 10.1214/22-aap1811
Jetlir Duraj, Michael Bar, V. Wachtel
{"title":"Invariance principles for integrated random walks conditioned to stay positive","authors":"Jetlir Duraj, Michael Bar, V. Wachtel","doi":"10.1214/22-aap1811","DOIUrl":"https://doi.org/10.1214/22-aap1811","url":null,"abstract":"Let $S(n)$ be a centered random walk with finite second moment. We consider the integrated random walk $T(n) = S(0)+S(1)+dots+S(n)$. We prove invariance principles for the meander and for the bridge of this process, under the condition that the integrated random walk remains positive. Furthermore, we prove the functional convergence of its Doob's $h$-transform to the $h$-transform of the Kolmogorov diffusion conditioned to stay positive.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43788790","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
Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields 弱依赖性平稳随机场的中心极限定理及其在边界和混合移动平均场中的应用
IF 1.8 2区 数学
Annals of Applied Probability Pub Date : 2020-07-21 DOI: 10.1214/21-aap1722
I. Curato, R. Stelzer, Bennet Stroh
{"title":"Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields","authors":"I. Curato, R. Stelzer, Bennet Stroh","doi":"10.1214/21-aap1722","DOIUrl":"https://doi.org/10.1214/21-aap1722","url":null,"abstract":"We obtain central limit theorems for stationary random fields which are based on the use of a novel measure of dependence called $theta$-lex weak dependence. We discuss hereditary properties for $theta$-lex and $eta$-weak dependence and illustrate the possible applications of the weak dependence notions to the study of the asymptotic properties of stationary random fields. Our general results are applied to mixed moving average fields (MMAF in short) and ambit fields. We show general conditions such that MMAF and ambit fields, with the volatility field being an MMAF or a $p$-dependent random field, are weakly dependent. For all the aforementioned models, we give a complete characterization of their weak dependence coefficients and sufficient conditions to obtain asymptotic normality of their sample moments. Finally, we give explicit computations of the weak dependence coefficients in the case of MSTOU and CARMA fields.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43700063","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: 5
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信