-
作者：OVERBECK, L; ROCKNER, M; SCHMULAND, B
作者单位：University of Alberta
摘要：We study a class of (nonsymmetric) Dirichlet forms (E, D(E)) having a space of measures as state space E and derive some general results about them. We show that under certain conditions they ''generate'' diffusion processes M. In particular, if M is ergodic and (E, D(E)) is symmetric w.r.t. quasi-every starting point, the large deviations of the empirical distribution of M are governed by E. We apply all of this to construct Fleming-Viot processes with interactive selection and prove some res...
-
作者：PEMANTLE, R; PERES, Y
作者单位：University of California System; University of California Berkeley
摘要：We study the behavior of random walk in random environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ratios of resistances of neighboring edges of a tree Gamma are i.i.d. random variables whose logarithms have mean zero and finite variance. Then the resulting RWRE is transient if simple random walk on Gamma is transient, but not vice versa We obtain general transience criteria for such walks, which...
-
作者：BALLY, V; MILLET, A; SANZSOLE, M
作者单位：Sorbonne Universite; University of Barcelona
摘要：The solution u(t, x) of a parabolic stochastic partial differential equation is a random element of the space C-alpha,C-beta of Holder continuous functions on [0, T] x [0, 1] of order (alpha = 1/4 - epsilon in the time variable and beta = 1/2 - epsilon in the space variable, for any epsilon > 0. We prove a support theorem in C-alpha,C-beta for the law of u. The proof is based on an approximation procedure in Holder norm (which should have its own interest) using a space-time polygonal interpol...
-
作者：CUZICK, J; GINE, E; ZINN, J
作者单位：University of Connecticut; University of Connecticut; Texas A&M University System; Texas A&M University College Station; Texas A&M University System; Texas A&M University College Station
摘要：Let X, X(i) be i.i.d. real random variables with EX(2) = infinity. Necessary and sufficient conditions in terms of the law of X are given for (1/gamma(n)) max(1 less than or equal to i 0 a.s. in general and for (1/gamma(n)) Sigma(1 less than or equal to i not equal j less than or equal to n) X(i)X(j) --> 0 a.s. when the variables X(i) are symmetric or regular and the normalizing sequence {gamma(n)} is (mildly) regular. The rates of a.s. convergence of sums and maxima of products turn out to be...
-
作者：REINERT, G
作者单位：University of Zurich
摘要：Let E be a locally compact Hausdorff space with countable basis and let (X(i))(i epsilon N) be a family of random elements on E with (1/n) Sigma(i=1)(n) L (X(i)) double right arrow(>)v mu(n --> infinity) for a measure mu with parallel to mu parallel to less than or equal to 1. Conditions are derived under which L ((1/n) Sigma(i=1)(n) (delta)X(i)) double right arrow(w) delta(mu)(n --> infinity), where delta(x), denotes the Dirac measure at x. The proof being based on Stein's method, there are g...
-
作者：SIMONELLI, I
摘要：Let S be a countable set and Lambda the collection of all subsets of S. We consider interacting particle systems (IPS) {eta(t)} on Lambda, with duals {<(eta)over tilde>(t)}, and duality equation P[\eta(t)(xi)boolean AND A\ odd] = (P) over tilde[\<(eta)over tilde>(A)(t) A boolean AND xi\ odd], xi, A subset of S, A finite. Under certain conditions we find all the extreme invariant distributions that arise as limits of translation invariant initial configurations. Specific systems will be conside...
-
作者：VERZANI, J
摘要：A slow point from the left for Brownian motion is a time during a given interval for which the oscillations of the path immediately to the left of this time are smaller than the typical ones, that is, those given by the local LIL. These slow points occur at random times during a given interval. For historical super-Brownian motion, the support at a fixed time contains an infinite collection of paths. This paper makes use of a branching process description of the support to investigate the slow...
-
作者：KERSTING, G; KLEBANER, FC
作者单位：University of Melbourne
摘要：We give sharp sufficient conditions for nonexplosions and explosions in Markov pure jump processes in terms of the holding time parameters and moments of the jump distributions.
-
作者：LIAO, M; ZHENG, WA
作者单位：University of California System; University of California Irvine
摘要：Let rho(t) be the radial part of a Brownian motion in an n-dimensional Riemannian manifold M starting at x and let T = T-epsilon be the first time t when rho(t) = epsilon. We show that E[rho(t boolean AND T)(2)] = nt - (1/6)S(x)t(2) + o(t(2)), as t down arrow 0, where S(x) is the scalar curvature. The same formula holds for E[rho(t)(2)] under some boundedness condition on M.
-
作者：HOUDRE, C; PEREZABREU, V
作者单位：CIMAT - Centro de Investigacion en Matematicas
摘要：We present covariance identities and inequalities for functionals of the Wiener and the Poisson processes. Using Malliavin calculus techniques, an expansion with a remainder term is obtained for the covariance of such functionals. Our results extend known identities and inequalities for functions of multivariate random vectors.
