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作者：Cheng, Dan; Xiao, Yimin
作者单位：Arizona State University; Arizona State University-Tempe; Michigan State University
摘要：Let { (X (t), Y(s)) : t is an element of T, s is an element of S } be an R2-valued, centered, unit-variance smooth Gaussian vector field, where T and S are compact rectangles in the Euclidean space. It is shown that, as u -> infinity , the joint excursion probability P{supt is an element of T X (t) >= u, sup s is an element of S Y(s) >= u } can be approximated by E{chi (Au)}, the expected Euler characteristic of the excursion set Au = { (t, s) is an element of T x S : X (t) >= u, Y(s) >= u } ,...
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作者：Banderier, Cyril; Kuba, Markus; Wallner, Michael
作者单位：Universite Paris 13; Technische Universitat Wien; Technische Universitat Wien
摘要：Multitudinous probabilistic and combinatorial objects are associated with generating functions satisfying a composition scheme F(z) = G(H(z)). The analysis becomes challenging when this scheme is critical (i.e., G and H are simultaneously singular). Motivated by many examples (random mappings, planar maps, directed lattice paths), we consider a natural extension of this scheme, namely F(z, u) = G(uH(z))M(z). We also consider a variant of this scheme, which allows us to analyse the number of H-...
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作者：Friesen, Martin; Jin, Peng
作者单位：Dublin City University; Beijing Normal-Hong Kong Baptist University
摘要：The Volterra square-root process on R-+(m) is an affine Volterra process with continuous sample paths. Under a suitable integrability condition on the resolvent of the second kind associated with the Volterra convolution kernel, we establish the existence of limiting distributions. In contrast to the classical square-root diffusion process, here the limiting distributions may depend on the initial state of the process. Our result shows that the nonuniqueness of limiting distributions is closel...
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作者：Qin, Qian
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix algebra exercises. It is found that in terms of asymptotic variance, the two-component random-scan Gibbs sampler is never much worse, and could be considerably better than its deterministic-scan counterpart, provided that the selection probability is appropriately...
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作者：Roberts, Asher
作者单位：City University of New York (CUNY) System
摘要：In this paper we quantify the rate of convergence in Selberg's central limit theorem for log |zeta (1/2 + it)| based on the method of proof given by the same rate of convergence of (log log log T )2/root log log T as Selberg in (In 1989) Univ (1992) 367-385) in the Kolmogorov distance by using the Dudley distance instead. We also prove the theorem for the multivariate case given by same rate of convergence as in the single variable case.
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作者：Ziliotto, Bruno
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
摘要：In a zero -sum stochastic game with signals (Repeated Games (2015) Cambridge Univ. Press, Chapter IV), at each stage, two adversary players make decisions and receive stage payoffs determined by these decisions and a variable called the state. The state follows a Markov chain controlled by both players. Actions and states are imperfectly observed by players, who receive private signals at each stage. Mertens (In Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, ...
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作者：Grotto, Francesco; Luongo, Eliseo; Romito, Marco
作者单位：University of Pisa; Scuola Normale Superiore di Pisa
摘要：We consider a system of N point vortices in a bounded domain with null total circulation, whose statistics are given by the canonical Gibbs ensemble at inverse temperature beta >= 0. We prove that the space-time fluctuation field around the (constant) mean field limit satisfies when N -> infinity a generalized version of two-dimensional Euler dynamics preserving the Gaussian energyenstrophy ensemble.
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作者：Leao, Dorival; Ohashi, Alberto; DE Souza, Francys a.
作者单位：Universidade de Brasilia
摘要：In this article, we present a general methodology for stochastic control problems driven by the Brownian motion filtration including non-Markovian and nonsemimartingale state processes controlled by mutually singular measures. The main result of this paper is the development of a numerical scheme for computing near-optimal controls associated with controlled Wiener functionals via a finite-dimensional approximation procedure. The approach does not require functional differentiability assumptio...
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作者：Erhard, Dirk; Reis, Guilherme
作者单位：Universidade Federal da Bahia; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We introduce a simple but powerful strategy to study processes driven by two or more reinforcement mechanisms in competition. We apply our method to two types of models: to nonconservative zero range processes on finite graphs, and to multi-particle random walks with positive and negative reinforcement on the edges. The results hold for a broad class of reinforcement functions, including those with superlinear growth. Our strategy consists in a comparison of the original processes with suitabl...
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作者：Nachmias, Asaf; Tang, Pengfei
作者单位：Tel Aviv University; Tianjin University
摘要：We study the spectral and diffusive properties of the wired minimal span-ning forest (WMSF) on the Poisson-weighted infinite tree (PWIT). LetMbethe tree containing the root in the WMSF on the PWIT and(Y-n)(n >= 0)be asimple random walk onMstarting from the root. We show that almost surelyMhasP[Y-2n=Y-0]=n-(3/4+o(1))and dist(Y-0,Y-n)=n(1/4+o(1))with highprobability. That is, the spectral dimension ofMis 3/2 and its typical dis-placement exponent is 1/4, almost surely. These confirm Addario-Berr...
