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作者：Ignatiouk-Robert, Irina; Loree, Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); CY Cergy Paris Universite
摘要：A complete representation of the Martin boundary of killed random walks on the quadrant N* x N* is obtained. It is proved that the corresponding full Martin compactification of the quadrant N* x N* is homeomorphic to the closure of the set {w = z/(1 +vertical bar z vertical bar) : Z is an element of N* x N*} in R(2). The method is based on a ratio limit theorem for local processes and large deviation techniques.
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作者：Kang, Weining; Ramanan, Kavita
作者单位：Carnegie Mellon University
摘要：For a class of stochastic differential equations with reflection for which a certain LP continuity condition holds with p > 1, it is shown that any weak solution that is a strong Markov process can be decomposed into the sum of a local martingale and a continuous, adapted process of zero p-variation. When p = 2, this implies that the reflected diffusion is a Dirichlet process. Two examples are provided to motivate such a characterization. The first example is a class of multidimensional reflec...
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作者：Comets, Francis; Popov, Serguei; Schuetz, Gunter M.; Vachkovskaia, Marina
作者单位：Universite Paris Cite; Universidade Estadual de Campinas; Helmholtz Association; Research Center Julich
摘要：We consider a stochastic billiard in a random tube which stretches to infinity in the direction of the first coordinate. This random tube is stationary and ergodic, and also it is supposed to be in some sense well behaved. The stochastic billiard can be described as follows: when strictly inside the tube, the particle moves straight with constant speed. Upon hitting the boundary, it is reflected randomly, according to the cosine law: the density of the outgoing direction is proportional to the...
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作者：Hug, Daniel; Schneider, Rolf
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Freiburg
摘要：A generalized version of a well-known problem of D. G. Kendall states that the zero cell of a stationary Poisson hyperplane tessellation in R(d), under the condition that it has lame volume, approximates with high probability a certain definite shape, which is determined by the directional distribution of the underlying hyperplane process. This result is extended here to typical k-faces of the tessellation, for k is an element of {2, ... , d - 1}. This requires the additional condition that th...
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作者：Fleischmann, Klaus; Mytnik, Leonid; Wachtel, Vitali
作者单位：Technion Israel Institute of Technology; University of Munich
摘要：For 0 < alpha <= 2, a super-alpha-stable motion X in R(d) with branching of index 1 + beta is an element of (1,2) is considered. Fix arbitrary t > 0. If d < alpha/beta, a dichotomy for the density function of the measure X(t) holds: the density function is locally Holder continuous if d = 1 and alpha > 1 + beta but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local Holder index.
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作者：Berard, Jean; Ramirez, Alejandro F.
作者单位：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; CNRS - National Institute for Mathematical Sciences (INSMI); Pontificia Universidad Catolica de Chile
摘要：We investigate the probabilities of large deviations for the position of the front in a stochastic model of the reaction X + Y -> 2X on the integer lattice in which Y particles do not move while X particles move as independent simple continuous time random walks of total jump rate 2. For a wide class of initial conditions, we prove that a large deviations principle holds and we show that the zero set of the rate function is the interval [0, nu vertical bar. where nu is the velocity of the fron...
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作者：Bryc, Wlodek; Wesolowski, Jacek
作者单位：University System of Ohio; University of Cincinnati; Warsaw University of Technology
摘要：We use orthogonality measures of Askey Wilson polynomials to construct Markov processes with linear regressions and quadratic conditional variances. Askey-Wilson polynomials are orthogonal martingale polynomials for these processes.
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作者：Valko, Benedek; Virag, Balint
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Toronto
摘要：We show that in the point process limit of the bolt eigenvalues of beta-ensembles of random matrices, the probability of having no eigenvalue ill a fixed interval of size lambda is given by (kappa beta + sigma(1))lambda(gamma beta) exp(-beta/64 lambda(2) + (beta/8-1/4)lambda) as lambda --> infinity, where gamma beta = 1/4(beta/2 + 2/beta -3) and kappa beta is an undetermined positive constant. This is a slightly corrected version of a prediction by Dyson 11 Math. Phys. 3 (1962) 157-1651. Our p...
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作者：Le Jan, Yves
作者单位：Universite Paris Saclay
摘要：We study the Poissonnian ensembles of Markov loops and the associated renormalized self intersection local times.
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作者：Matoussi, Anis; Stoica, Lucretiu
作者单位：Le Mans Universite; Romanian Academy; University of Bucharest; Institute of Mathematics of the Romanian Academy; University of Bucharest
摘要：We prove an existence and uniqueness result for the obstacle problem of quasi linear parabolic stochastic PDEs. The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic differential equation.
