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作者：Mytnik, L
作者单位：University of British Columbia
摘要：The uniqueness in law for the equation partial derivative X-t/partial derivative t = 1/2 Delta X-t + X-t(gamma)(W) over dot is established for 1/2 < gamma < 1. The proof uses a duality technique and requires the construction of an approximating sequence of dual processes.
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作者：Li, SM; Ogura, Y
作者单位：Saga University
摘要：The purpose of this paper is to prove some convergence theorems of closed and convex set valued sub- and supermartingales in the Kuratowski-Mosco sense. To get submartingale convergence theorems, we give sufficient conditions for the Kudo-Aumann integral and Hiai-Umegaki conditional expectation to be closed both for compact convex set valued random variables and for closed convex set valued random variables. We also give an example of a bounded closed convex set valued random variable whose Ku...
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作者：Dawson, DA; Perkins, EA
作者单位：University of British Columbia
摘要：We study a system of two interacting populations which undergo random migration and mutually catalytic branching. The branching rate of one population at a site is proportional to the mass of the other population at the site. The system is modelled by an infinite system of stochastic differential equations, allowing symmetric Markov migration, if the set of sites is discrete (Z(d)), or by a stochastic partial differential equation with Brownian migration if the set of sites is the real line. A...
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作者：Qian, J
作者单位：Bucknell University
摘要：The p-variation of a function f is the supremum of the sums of the pth powers of absolute increments of f over nonoverlapping intervals. Let F be a continuous probability distribution function. Dudley has shown that the p-variation of the empirical process is bounded in probability as n --> infinity if and only if p > 2, and for 1 less than or equal to p less than or equal to 2, the p-variation of the empirical process is at least n(1-p/2) and is at most of the order n(1-p/2)(log log n)(p/2) i...
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作者：Dhersin, JS; Le Gall, JF
作者单位：Universite Paris Cite; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We prove a Kolmogorov test for super-Brownian motion started at the Dirac mass at the origin. More precisely, we determine the functions g such that for all t small enough, the support of the process at time t will be contained in the ball of radius g(t) centered at 0. As a consequence, we get a necessary and sufficient condition for the existence in certain spacetime domains of a solution of the associated semilinear partial differential equation that blows up at the origin.
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作者：Rezakhanlou, F
作者单位：University of California System; University of California Berkeley
摘要：We study a one-dimensional particle system in which particles travel deterministically in between stochastic collisions. As the total number of particles tends to infinity, the empirical density converges to a solution of a discrete Boltzmann equation. We establish the large deviation principle for the convergence with a rate function that is given by a Variational formula. Some of the properties of the rate function are discussed and a nonvariational expression for the rate function is given.
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作者：Piau, D
作者单位：Universite Claude Bernard Lyon 1
摘要：The simple random walk on a supercritical Galton-Watson tree is transient when the tree is infinite. Moreover, there exist regeneration times, that is, times when the walk crosses an edge for the first and the last time. We prove that the distance and the range of the walk satisfy functional central limit theorems under the annealed law GP. This result is a consequence of estimates of the law of the first regeneration time tau(R). We show that there exist positive c, c', alpha and beta such th...
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作者：Freidlin, M; Weber, M
作者单位：University System of Maryland; University of Maryland College Park; Technische Universitat Dresden
摘要：Degenerate white noise perturbations of Hamiltonian systems in R-2 are studied. In particular perturbations of a nonlinear oscillator with 1 degree of freedom are considered. If the oscillator has more than one stable equilibrium, the long time behavior of the system is defined by a diffusion process on a graph. Inside the edges the process is defined by a standard averaging procedure, but to define the process for all t > 0, one should add gluing conditions at the vertices. Calculation of the...
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作者：Haggstrom, O; Mossel, E
作者单位：Chalmers University of Technology; Hebrew University of Jerusalem
摘要：A few years ago, Grimmett, Resten and Zhang proved that for supercritical bond percolation on Z(3), simple random walk on the infinite cluster is a.s. transient. We generalize this result to a class of wedges in Z(3) including, for any epsilon is an element of (0, 1), the wedge W-epsilon = {(x, y, z) is an element of Z(3): x greater than or equal to 0, \z\ less than or equal to x(epsilon)} which can be thought of as representing a (2 + epsilon)-dimensional lattice, Our proof builds on recent w...
