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作者：Bailleul, Ismael; Franchi, Jacques
作者单位：University of Cambridge; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：Some general Lorentz covariant operators, associated to the so-called Theta (or Xi)-relativistic diffusions and making sense in any Lorentzian manifold, have been introduced by Franchi and Le Jan [Comm. Pure Appl. Math. 60 (2007) 187-251], Franchi and Le Jan [Curvature diffusions in general relativity (2010). Unpublished manuscript]. Only a few examples have been studied so far. We provide in this work some nonexplosion criteria for these diffusions, which can be used in generic cases.
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作者：Ceillier, Gael
摘要：Let X be a stationary process with finite state-space A. Bressaud et al. [Ann. Probab. 34 (2006) 1589-1600] recently provided a sufficient condition for the natural filtration of X to be standard when A has size 2. Their condition involves the conditional laws p(.vertical bar x) of X-0 conditionally on the whole past (X-k)(k <=-1) = x and controls the strength of the influence of the old past of the process on its present X-0. It involves the maximal gaps between p(.vertical bar x) and p(.vert...
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作者：Chen, Yu-Ting; Delmas, Jean-Francois
作者单位：University of British Columbia; Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Universite Gustave-Eiffel
摘要：We consider an elementary model of random size varying population governed by a stationary continuous-state branching process. We compute the distributions of various variables related to the most recent common ancestor (MRCA): the time to the MRCA, the size of the current population and the size of the population just before the MRCA. In particular we observe a natural mild bottleneck effect as the size of the population just before the MRCA is stochastically smaller than the size of the curr...
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作者：Bettinelli, Jeremie
作者单位：Universite Paris Saclay
摘要：We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given g, we consider, for every n >= 1, a random quadrangulation q(n) uniformly distributed over the set of all rooted bipartite quadrangulations of genus g with n faces. We view it as a metric space by endowing its set of vertices with the graph metric. As n tends to infinity, this metric space, with distances rescaled by the factor n(-1/4), converges in distribution, at least along some subsequence, toward...
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作者：Kuwada, Kazumasa
作者单位：Ochanomizu University
摘要：We study an approximation by time-discretized geodesic random walks of a diffusion process associated with a family of time-dependent metrics on manifolds. The condition we assume on the metrics is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow, and no further a priori curvature bound is required. As an application, we construct a coupling by reflection which yields a nice estimate of coupling time, and hence a...
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作者：Basrak, Bojan; Krizmanic, Danijel; Segers, Johan
作者单位：University of Zagreb; University of Rijeka; Universite Catholique Louvain
摘要：Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version of this is known to be true as well, the limit process being a stable Levy process. The main result in the paper is that for a stationary, regularly varying sequence for which clusters of high-threshold excesses can be broken down into asymptotically indepe...
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作者：Cohen, Samuel N.; Elliott, Robert J.
作者单位：University of Oxford; University of Adelaide; University of Calgary
摘要：We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic variations of martingales or of the measure integrating the driver. We present conditions for existence and uniqueness of square-integrable solutions, using Lipschitz continuity of the driver. These conditions unite the requirements for existence in continuous and ...
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作者：Diaconis, Persi; Ram, Arun
作者单位：Stanford University; Stanford University; University of Melbourne
摘要：The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in the power sum polynomials. The Markov chain has stationary distribution a new two-parameter family of measures on partitions, the inverse of the Macdonald weight (rescaled). The uniform distribution on cycles of permutations and the Ewens sampling formula ar...
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作者：Williams, John D.
作者单位：Indiana University System; Indiana University Bloomington
摘要：Let mu be a probability measure on the real line. In this paper we prove that there exists a decomposition mu = mu(0) boxed plus mu(1) boxed plus ... boxed plus mu(n) boxed plus ... such that mu(0) is infinitely divisible, and mu(i) is indecomposable for i >= 1. Additionally, we prove that the family of all boxed plus-divisors of a measure mu is compact up to translation. Analogous results are also proven in the case of multiplicative convolution.
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作者：Albeverio, Sergio; Kusuoka, Seiichiro
作者单位：University of Bonn; Kyoto University
摘要：The present paper is concerned with diffusion processes running on tubular domains with conditions on nonreaching the boundary, respectively, reflecting at the boundary, and corresponding processes in the limit where the thin tubular domains are shrinking to graphs. The methods we use are probabilistic ones. For shrinking, we use big potentials, respectively, reflection on the boundary of tubes. We show that there exists a unique limit process, and we characterize the limit process by a second...
