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作者：Vasdekis, G.; Roberts, G. O.
作者单位：University of London; University College London; University of Warwick
摘要：The Zig-Zag process is a piecewise deterministic Markov process, efficiently used for simulation in an MCMC setting. As we show in this article, it fails to be exponentially ergodic on heavy tailed target distributions. We introduce an extension of the Zig-Zag process by allowing the process to move with a nonconstant speed function s, depending on the current state of the process. We call this process Speed Up Zig-Zag (SUZZ). We provide conditions that guarantee stability properties for the S...
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作者：Jahnel, Benedikt; Koeppl, Jonas
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider irreversible translation-invariant interacting particle systems on the d-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy conditions on the rates and the specification we prove that zero relative entropy loss of a translation-invariant measure implies that the measure is Gibbs w.r.t. the same specification as the time-stationary Gibbs measure. As an application, we obtain the att...
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作者：Blancas, Airam; Gufler, Stephan; Kliem, Sandra; Tran, Viet chi; Wakolbinger, Anton
作者单位：Instituto Tecnologico Autonomo de Mexico; Goethe University Frankfurt; Leipzig University; Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：For a continuous state branching process with two types of individuals which are subject to selection and density dependent competition, we characterize the joint evolution of population size, type configurations and genealogies as the unique strong solution of a system of SDEs. Our construction is achieved in the lookdown framework and provides a synthesis as well as a generalization of cases considered separately in two seminal papers by Donnelly and Kurtz (Ann. Appl. Probab. 9 (1999) 1091-1...
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作者：Bai, Tianyi; Hu, Yueyun
作者单位：New York University; NYU Shanghai
摘要：Let R-n be the range of a critical branching random walk with n particles on Z(d) , which is the set of sites visited by a random walk indexed by a critical Galton- Watson tree conditioned on having exactly n vertices. For d is an element of {3, 4, 5}, we prove that n - (d-2)/(4) cap((d)) (R-n), the renormalized capacity of Rn, converges in law to the capacity of the support of the integrated super-Brownian excursion. The proof relies on a study of the intersection probabilities between the cr...
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作者：Feireisl, Eduard; Cova-medvidova, Maria Luka
作者单位：Czech Academy of Sciences; Institute of Mathematics of the Czech Academy of Sciences; Johannes Gutenberg University of Mainz
摘要：We propose a stochastic collocation method based on the piecewise con -stant interpolation on the probability space combined with a finite volume method to solve the compressible Navier-Stokes system at the nodal points. We show convergence of numerical solutions to a statistical solution of the Navier-Stokes system on condition that the numerical solutions are bounded in probability. The analysis uses the stochastic compactness method based on the Skorokhod/Jakubowski representation theorem a...
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作者：Liu, Song-hao; Zhang, Zhuo-song
作者单位：Southern University of Science & Technology
摘要：We establish Cramer-type moderate deviation theorems for the sums of locally dependent random variables and combinatorial central limit theorems. Optimal error bounds and convergence ranges are obtained under some mild exponential moment conditions. Our main results are more general or sharper than the results in the literature. The main results follow from a more gen-eral Cramer-type moderate deviation theorem for dependent random variables without any boundedness assumptions, which is of ind...
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作者：Conforti, Giovanni
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We investigate the long time behavior of weakly dissipative semilinear Hamilton-Jacobi-Bellman (HJB) equations and the turnpike property for the corresponding stochastic control problems. To this aim, we develop a proba-bilistic approach based on a variant of coupling by reflection adapted to the study of controlled diffusion processes. We prove existence and uniqueness of solutions for the ergodic Hamilton-Jacobi-Bellman equation and different kind of quantitative exponential convergence resu...
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作者：Lehec, Joseph
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Poitiers
摘要：We prove nonasymptotic polynomial bounds on the convergence of the Langevin Monte Carlo algorithm in the case where the potential is a convex function which is globally Lipschitz on its domain, typically the maximum of a finite number of affine functions on an arbitrary convex set. In particular the potential is not assumed to be gradient Lipschitz, in contrast with most existing works on the topic.
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作者：Ligget, Thomas m.; Tang, Wenpin
作者单位：University of California System; University of California Los Angeles; Columbia University
摘要：This paper is concerned with symmetric 1-dependent colorings of the dray star graph S-d for d >= 2. We compute the critical point of the 1-dependent hard-core processes on S-d, which gives a lower bound for the number of colors needed for a 1-dependent coloring of S-d. We provide an explicit construction of a 1-dependent q-coloring for any q >= 5 of the infinite subgraph S-(1,1,infinity)(3), which is symmetric in the colors and whose restriction to any path is some symmetric 1-dependent q-colo...
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作者：Analytis, Pantelis P.; Gelastopoulos, Alexandros; Stojic, Hrvoje
作者单位：University of Southern Denmark; Pompeu Fabra University
摘要：We study a discrete-time Markov process X-n is an element of R-d for which the distribution of the future increments depends only on the relative ranking of its components (descending order by value). We endow the process with a rich-get-richer assumption and show that, together with a finite second moments assumption, it is enough to guarantee almost sure convergence of X-n/n. We characterize the possible limits if one is free to choose the initial state and we give a condition under which th...
