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作者：Bramson, M; Cox, JT; Greven, A
作者单位：University of Wisconsin System; University of Wisconsin Madison; Syracuse University; University of Erlangen Nuremberg
摘要：We consider two critical spatial branching processes on R-d: critical branching Brownian motion, and the critical Dawson-Watanabe process. A basic feature of these processes is that their ergodic behavior is highly dimension dependent. It is known that in low dimensions, d less than or equal to 2, the only invariant measure is delta(0), the unit point mass on the empty state. In high dimensions, d greater than or equal to 3, there is a family {nu(0), theta is an element of [0, infinity)} of ex...
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作者：Graham, C; Méléard, S
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Sorbonne Universite
摘要：We specify the Markov process corresponding to a generalized mollified Boltzmann equation with general motion between collisions and nonlinear bounded jump (collision) operator, and give the nonlinear martingale problem it solves. We consider various Linear interacting particle systems in order to approximate this nonlinear process. We prove propagation of chaos, in variation norm on path space with a precise rate of convergence, using coupling and interaction graph techniques and a representa...
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作者：Bolthausen, E; Schmock, U
作者单位：University of Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Let {X-t}(t greater than or equal to 0) be a symmetric, nearest-neighbor random walk on Z(d) with exponential holding times of expectation 1/d, starting at the origin. For a potential V: Z(d) --> [0, infinity) with finite and nonempty support, define transformed path measures by d (P) over cap(T) = exp(T(-1)integral(0)(T)integral(0)(T)V(X-s - X-t)ds/dt)dP/Z(T) for T > 0, where ZT is the normalizing constant. If d = 1 or if the self-attraction is sufficiently strong, then \\X-t\\(infinity) has ...
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作者：Chen, ZQ; Durrett, R; Ma, G
作者单位：Cornell University
摘要：We study a family of differential operators (L-alpha, alpha greater than or equal to 0) in the unit bah D of C-n with n greater than or equal to 2 that generalize the classical Laplacian, alpha = 0, and the conformal Laplacian, alpha = 1/2 (that is, the Laplace-Beltrami operator for Bergman metric in D). Using the diffusion processes associated with these (degenerate) differential operators, the boundary behavior of L-alpha-harmonic functions is studied in a unified way for 0 less than or equa...
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作者：Mohammed, SEA; Scheutzow, MKR
作者单位：Southern Illinois University System; Southern Illinois University; Technical University of Berlin
摘要：we give several examples and examine case studies of linear stochastic functional differential equations. The examples fall into two broad classes: regular and singular, according to whether an underlying stochastic semiflow exists or not. In the singular case, we obtain upper and lower bounds on the maximal exponential growth rate <(lambda)over bar>(1) (sigma) of the trajectories expressed in terms of the noise variance sigma. Roughly speaking we show that for small sigma, <(lambda)over bar>(...
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作者：Choi, KP; Klass, MJ
作者单位：National University of Singapore; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Let Phi(.) be a nondecreasing convex function on [0, infinity). We show that for any integer n greater than or equal to 1 and real a, E Phi((M-n - a)(+)) less than or equal to 2E Phi((S-n - a)(+)) - Phi(0) and E(M-n boolean OR med S-n) less than or equal to E\S-n - med S-n\. where X-1, X-2,... are any independent mean zero random variables with partial sums S-0 = 0, S-k = X-1 +...+ X-k and partial sum maxima M-n = max(0 less than or equal to k less than or equal to n) S-k. There are various in...
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作者：van der Hofstad, R; den Hollander, F; König, W
作者单位：Utrecht University; Radboud University Nijmegen; Technical University of Berlin
摘要：The Edwards model in one dimension is a transformed path measure for standard Brownian motion discouraging self-intersections. We prove a central limit theorem for the endpoint of the path, extending a law of large numbers proved by Westwater. The scaled variance is characterized in terms of the largest eigenvalue of a one-parameter family of differential operators, introduced and analyzed by van der Hofstad and den Hollander. Interestingly, the scaled variance turns out to be independent of t...
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作者：Liggett, TM
作者单位：University of California System; University of California Los Angeles
摘要：Interacting particle systems is by now a mature area of probability theory, but one that is still very active. We begin this paper by explaining how models from this area arise in fields such as physics and biology. We turn then to a discussion of both older and more recent results about them, concentrating on contact processes, voter models, and exclusion processes. These processes are among the most studied in the field, and have the virtue of relative simplicity in their description, which ...
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作者：Donati-Martin, C; Yor, M
作者单位：Sorbonne Universite
摘要：We develop some topics about Brownian motion with a particular emphasis on the study of principal values of Brownian local times. We show some links between principal values and Doob's h-transforms of Brownian motion, for nonpositive harmonic functions h. We also give a survey and complement some martingale approaches to Ray-Knight theorems for local times.
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作者：Latala, R
作者单位：University of Warsaw
摘要：For the sum S = Sigma X-i of a sequence (X-i) of independent symmetric (or nonnegative) random variables, we give lower and upper estimates of moments of S. The estimates are exact, up to some universal constants, and extend the previous results for particular types of variables X-i.
