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作者：Chu, Raymond; Kim, Inwon; Kim, Young-Heon; Nam, Kyeongsik
作者单位：University of California System; University of California Los Angeles; University of British Columbia; Korea Advanced Institute of Science & Technology (KAIST)
摘要：We study the nonlocal Stefan problem, where the phase transition is described by a nonlocal diffusion as well as the change of enthalpy functions. By using a stochastic optimization approach introduced in Kim and Kim (The Stefan problem and free targets of optimal Brownian martingale transport, 2021. arXiv preprint arXiv:2110.03831), we construct global-time weak solutions and give a probabilistic interpretation for the solutions. An important ingredient in our analysis is a probabilistic inte...
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作者：van den Berg, Jacob; Nolin, Pierre
作者单位：Centrum Wiskunde & Informatica (CWI); City University of Hong Kong
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作者：Chiusole, Gideon; Friz, Peter K.
作者单位：Technical University of Munich; Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Wiener spaces are in many ways the decisive setting for fundamental results on Gaussian measures: large deviations (Schilder), quasi-invariance (Cameron-Martin), differential calculus (Malliavin), support description (Stroock-Varadhan), concentration of measure (Fernique), ...Analogues of these classical results have been derived in the enhanced context of Gaussian rough paths and, more recently, regularity structures equipped with Gaussian models. The aim of this article is to propose a simil...
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作者：Dembin, Barbara; Severo, Franco
作者单位：Universites de Strasbourg Etablissements Associes; Centre National de la Recherche Scientifique (CNRS); Universite de Strasbourg; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove that the supercritical phase of Voronoi percolation on R-d, d >= 3, is well behaved in the sense that for every p>p(c)(d) local uniqueness of macroscopic clusters happens with high probability. As a consequence, truncated connection probabilities decay exponentially fast and percolation happens on sufficiently thick 2D slabs. This is the analogue of the celebrated result of Grimmett and Marstrand for Bernoulli percolation and serves as the starting point for renormalization techniques...
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作者：Grazieschik, P.; Matetski, K.; Weber, H.
作者单位：University of Bath; Michigan State University; University of Munster
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作者：Prevost, Alexis; Rodriguez, Pierre-Francois; Sousi, Perla
作者单位：University of Bonn; Imperial College London; University of Cambridge
摘要：Let X be a random walk on the torus of side length N in dimension d >= 3 with uniform starting point, and t(cov) be the expected value of its cover time, which is the first time that X has visited every vertex of the torus at least once. For alpha> 0, the set L-alpha of alpha-late points consists of those points not visited by X at time alpha t(cov). We prove the existence of a value alpha & lowast; is an element of ( 1/2 , 1) across which L-alpha trivialises as follows: for all alpha>alpha & ...
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作者：Sojmark, Andreas; Wunderlich, Fabrice
作者单位：University of London; London School Economics & Political Science; University of Oxford
摘要：We provide criteria for It & ocirc; integration to behave continuously with respect to Skorokhod's J1 and M1 topologies, when the integrands and integrators converge weakly or in probability. The results are novel in the M1 setting and unify existing theories in the J1 case. Beyond sufficient criteria, we present an example of uniformly convergent martingale integrators for which the continuity breaks down. Moreover, we show that, for families of local martingales, M1 tightness in fact implies...
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作者：Rhee, Chang-Han; Ryu, Jeeho; Seo, Insuk
作者单位：Northwestern University; Seoul National University (SNU); Seoul National University (SNU); Seoul National University (SNU); Korea Institute for Advanced Study (KIAS)
摘要：Kesten's stochastic recurrent equation is a classical subject of research in probability theory and its applications. Recently, it has garnered attention as a model for stochastic gradient descent with a quadratic objective function and the emergence of heavy-tailed dynamics in machine learning. This context calls for analysis of its asymptotic behavior under both negative and positive Lyapunov exponents. This paper studies the exit times of the Kesten's stochastic recurrence equation in both ...
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作者：Cao, Shiping; Chen, Zhen-Qing
作者单位：Chinese University of Hong Kong; University of Washington; University of Washington Seattle
摘要：Starting with a transient irreducible diffusion process X0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X<^>0$$\end{document} on a locally compact separable metric space (D, d), one can construct a canonical symmetric reflected diffusion process X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasy...
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作者：Forsstrom, Malin P.; Gantert, Nina; Steif, Jeffrey E.
作者单位：Chalmers University of Technology; University of Gothenburg
