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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 Unpublished manuscript].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：Heuser, Aaron
作者单位：National Institutes of Health (NIH) - USA
摘要：This paper examines the existence of the self-intersection local time for a superprocess over a stochastic flow in dimensions d <= 3, which through constructive methods, results in a Tanaka-like representation. The superprocess over a stochastic flow is a superprocess with dependent spatial motion, and thus Dynkin's proof of existence, which requires multiplicity of the log-Laplace functional, no longer applies. Skoulakis and Adler's method of calculating moments is extended to higher moments,...
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作者：Chen, Zhen-Qing; Fitzsimmons, Patrick J.; Kuwae, Kazuhiro; Zhang, Tu-Sheng
作者单位：University of Washington; University of Washington Seattle; University of California System; University of California San Diego; Kumamoto University; University of Manchester
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作者：Seppaelaeinen, Timo
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We study a (1 + 1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the last-passage percolation model with exponential or geometric weights is special among growth models, namely, both permit explicit calculations. With appropriate boundary conditions, the polymer with log-gamma weights satisfies an analogue of Burke's theorem for queues. Building on this, we prove ...
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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：Roeckner, Michael; Zhu, Rong-Chan; Zhu, Xiang-Chan
作者单位：University of Bielefeld; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Peking University
摘要：In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur Rend. Lincei (9) Mat. Appl. 21 (2010) 405-414] by using Dirichlet form theory. By this definition, we can consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Gamma in a Hilbert space H. We prove the existence and uniqueness of a s...
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作者：Budhiraja, Amarjit; Dupuis, Paul; Fischer, Markus
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University
摘要：We study large deviation properties of systems of weakly interacting particles modeled by Ito stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures converges, as the number of particles tends to infinity, to the weak solution of an associated McKean-Vlasov equation. We derive a large deviation principle via the weak convergence approach. The proof, which avoids discretization arguments, is based on a representation ...
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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：Faggionato, Alessandra; Martinelli, Fabio; Roberto, Cyril; Toninelli, Cristina
作者单位：Sapienza University Rome; Roma Tre University; Universite Gustave-Eiffel; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：Motivated by several models introduced in the physics literature to study the nonequilibrium coarsening dynamics of one-dimensional systems, we consider a large class of hierarchical coalescence processes (HCP). An HCP consists of an infinite sequence of coalescence processes {xi((n))(.)}(n >= 1); each process occurs in a different epoch (indexed by n) and evolves for an infinite time, while the evolution in subsequent epochs are linked in such a way that the initial distribution of xi((n+1)) ...
