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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)) ...
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作者：Pardoux, Etienne; Piatnitski, Andrey
作者单位：Aix-Marseille Universite; UiT The Arctic University of Tromso
摘要：In this paper we study the homogenization of a nonautonomous parabolic equation with a large random rapidly oscillating potential in the case of one-dimensional spatial variable. We show that if the potential is a statistically homogeneous rapidly oscillating function of both temporal and spatial variables, then, under proper mixing assumptions, the limit equation is deterministic, and convergence in probability holds. To the contrary, for the potential having a microstructure only in one of t...
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作者：Privault, Nicolas
作者单位：Nanyang Technological University
摘要：We prove a Girsanov identity on the Poisson space for anticipating transformations that satisfy a strong quasi-nilpotence condition. Applications are given to the Girsanov theorem and to the invariance of Poisson measures under random transformations. The proofs use combinatorial identities for the central moments of Poisson stochastic integrals.
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作者：Roy, Emmanuel
作者单位：Universite Paris Cite
摘要：We give a second look at stationary stable processes by interpreting the self-similar property at the level of the Levy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences.
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作者：Dawson, Donald A.; Li, Zenghu
作者单位：Carleton University; Beijing Normal University
摘要：We first prove some general results on pathwise uniqueness, comparison property and existence of nonnegative strong solutions of stochastic equations driven by white noises and Poisson random measures. The results are then used to prove the strong existence of two classes of stochastic flows associated with coalescents with multiple collisions, that is, generalized Fleming-Viot flows and flows of continuous-state branching processes with immigration. One of them unifies the different treatment...
