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作者：Budhiraja, Amarjit; Dupuis, Paul; Ganguly, Arnab
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University; University of Louisville
摘要：Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive functionals of a PRM.
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作者：Hachem, Walid; Hardy, Adrien; Najim, Jamal
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS); Royal Institute of Technology; Universite Gustave-Eiffel; ESIEE Paris; Institut Polytechnique de Paris; Ecole des Ponts ParisTech
摘要：We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. In this setting, the support of the limiting eigenvalue distribution may have several connected components. Under mild conditions for the population matrices, we show that for every generic positive edge of that support, there exists an extremal eigenvalue which converges almost surely toward that edge and fluctuates according to the Tracy-Widom law at the scale N...
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作者：Miller, Jason; Sheffield, Scott
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：Given a simply connected planar domain D, distinct points x, y is an element of partial derivative D, and kappa > 0, the Schramm-Loewner evolution SLE kappa is a random continuous non-self-crossing path in (D) over bar from x to y. The SLE kappa (rho(1); rho(2)) processes, defined for rho(1), rho(2) > -2, are in some sense the most natural generalizations of SLE kappa. When kappa <= 4, we prove that the law of the time-reversal of an SLE kappa (rho(1); rho(2)) from x to y is, up to parameteriz...
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作者：Da Prato, G.; Flandoli, F.; Rockner, M.; Veretennikov, A. Yu.
作者单位：Scuola Normale Superiore di Pisa; University of Pisa; University of Bielefeld; University of Leeds; HSE University (National Research University Higher School of Economics); Kharkevich Institute for Information Transmission Problems of the RAS
摘要：We prove pathwise uniqueness for a class of stochastic differential equations (SDE) on a Hilbert space with cylindrical Wiener noise, whose non-linear drift parts are sums of the sub-differential of a convex function and a bounded part. This generalizes a classical result by one of the authors to infinite dimensions. Our results also generalize and improve recent results by N. Champagnat and P. E. Jabin, proved in finite dimensions, in the case where their diffusion matrix is constant and nond...
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作者：Ren, Jiagang; Wu, Jing
作者单位：Sun Yat Sen University
摘要：In this paper we prove an approximate continuity result for stochastic differential equations with normal reflections in domains satisfying Saisho's conditions, which together with the Wong-Zakai approximation result completes the support theorem for such diffusions in the uniform convergence topology. Also by adapting Millet and Sanz-Sole's idea, we characterize in Holder norm the support of diffusions reflected in domains satisfying the Lions-Sznitman conditions by proving limit theorems of ...
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作者：Debussche, Arnaud; Hofmanova, Martina; Vovelle, Julien
作者单位：Ecole Normale Superieure de Rennes (ENS Rennes); Max Planck Society; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we adapt the notion of kinetic formulation and kinetic solution and develop a well-posedness theory that includes also an L-1-contraction property. In comparison to the previous works of the authors concerning stochastic hyperbolic conservation laws [J. Funct. Anal. 259 (2010) 1014-1042] and semilinear degenerate parab...
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作者：Jirak, Moritz
作者单位：Humboldt University of Berlin
摘要：Let {X-k}(k >= Z) be a stationary sequence. Given p is an element of (2, 3] moments and a mild weak dependence condition, we show a Berry-Esseen theorem with optimal rate n(p/2-1). For p >= 4, we also show a convergence rate of n(1/2) in L-q-norm, where q >= 1. Up to log n factors, we also obtain nonuniform rates for any p > 2. This leads to new optimal results for many linear and nonlinear processes from the time series literature, but also includes examples from dynamical system theory. The ...
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作者：Chleboun, Paul; Faggionato, Alessandra; Martinelli, Fabio
作者单位：University of Warwick; University of Warwick; Sapienza University Rome; Roma Tre University
摘要：We consider a class of kinetically constrained interacting particle systems on Z(d) which play a key role in several heuristic qualitative and quantitative approaches to describe the complex behavior of glassy dynamics. With rate one and independently among the vertices of Z(d), to each occupation variable eta(x) is an element of {0, 1} a new value is proposed by tossing a (1 - q)-coin. If a certain local constraint is satisfied by the current configuration the proposed move is accepted, other...
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作者：Leonard, Christian
作者单位：Universite Paris Saclay
摘要：This paper is about the construction of displacement interpolations of probability distributions on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence of entropy minimization problems under marginal constraints, called Schrodinger problems, which are associated with random walks. Displacement interpolations are defined as the limit of the time-marginal flows of the solutions to...
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作者：Lupu, Titus
作者单位：Universite Paris Saclay
摘要：It was shown by Le Jan that the occupation field of a Poisson ensemble of Markov loops (loop soup) of parameter 1/2 associated to a transient symmetric Markov jump process on a network is half the square of the Gaussian free field. We construct a coupling between these loops and the free field such that an additional constraint holds: the sign of the free field is constant on each cluster of loops. As a consequence of our coupling we deduce that the loop clusters of parameter 1/2 do not percol...
