-
作者：Athreya, S; Tribe, R
作者单位：University of British Columbia; University of Warwick
摘要：We establish a duality relation for the moments of bounded solutions to a class of one-dimensional parabolic stochastic partial differential equations. The equations are driven by multiplicative space-time white noise, with a non-Lipschitz multiplicative functional. The dual process is a system of branching Brownian particles. The same method can be applied to show uniqueness in law for a class of non-Lipschitz finite dimensional stochastic differential equations.
-
作者：Gravner, J; Quastel, J
作者单位：University of California System; University of California Davis; University of Toronto
摘要：Generalized internal diffusion limited aggregation is a stochastic growth model on the lattice in which a finite number of sites act as Poisson sources of particles which then perform symmetric random walks with an attractive zero-range interaction until they reach the first site which has been visited by fewer than a particles, at which point they stop. Sites on which particles are frozen constitute the occupied set. We prove that in appropriate regimes the particle density has a hydrodynamic...
-
作者：Latala, R; Zinn, J
作者单位：University of Warsaw; Texas A&M University System; Texas A&M University College Station
摘要：Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the strong law of large numbers for (symmetrized) U-statistics. We also obtain necessary and sufficient conditions for the a.s. convergence of series of an analogous form.
-
作者：Klass, MJ; Nowicki, K
作者单位：University of California System; University of California Berkeley; Lund University
摘要：Let Phi be a symmetric function, nondecreasing on [0, infinity) and satisfying a Delta (2) growth condition, (X-1, Y-1), (X-2, Y-2),...,(X-n, Y-n) be independent random vectors such that (for each 1 less than or equal to i less than or equal to n) either Y-i = X-i or Y-i is independent of all the other variates, and the marginal distributions of {X-i} and {Y-j} are otherwise arbitrary. Let {f(ij)(x, y)}(1 less than or equal toi, j less than or equal ton) be any array of real valued measurable ...
-
作者：Arratia, R; Barbour, AD; Tavaré, S
作者单位：University of Southern California; University of Zurich
摘要：Under very mild conditions, we prove that the limiting behavior of the component counts in a decomposable logarithmic combinatorial structure conforms to a single, unified pattern, which includes functional central limit theorems, Erdas-Turan laws, Poisson-Dirichlet limits for the large components and Poisson approximation in total variation for the total number of components. Our approach is entirely probabilistic, and the conditions can readily be verified in practice.
-
作者：Ben Arous, G; Ramírez, AF
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Pontificia Universidad Catolica de Chile
摘要：We consider a model of diffusion in random media with a two-way coupling (i.e., a model in which the randomness of the medium influences the diffusing particles and where the diffusing particles change the medium). In this particular model, particles are injected at the origin with a time-dependent rate and diffuse among random traps. Each trap has a finite (random) depth, so that when it has absorbed a finite (random) number of particles it is saturated, and it no longer acts as a trap. This ...
-
作者：Cranston, M; Wang, FY
作者单位：University of Rochester; Beijing Normal University
摘要：It is proved in this paper that a weak parabolic Harnack inequality for a Markov semigroup implies the existence of a coupling and a shift coupling for the corresponding process with equal chances of success. This implies equality of the tail and invariant sigma -fields for the diffusion as well as equality of the class of bounded parabolic functions and the class of bounded harmonic functions.
-
作者：Jacod, J; Méléard, S; Protter, P
作者单位：Sorbonne Universite; Universite Paris Nanterre; Purdue University System; Purdue University
摘要：Stochastic integral representation of martingales has been undergoing a renaissance due to questions motivated by stochastic finance theory. In the Brownian case one usually has formulas (of differing degrees of exactness) for the predictable integrands. We extend some of these to Markov cases where one does not necessarily have stochastic integral representation of all martingales. Moreover we study various convergence questions that arise naturally from (for example) approximations of price ...
-
作者：Eisenbaum, N; Kaspi, H; Marcus, MB; Rosen, J; Shi, Z
作者单位：Sorbonne Universite; City University of New York (CUNY) System; City College of New York (CUNY); Technion Israel Institute of Technology; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：Let X be a strongly symmetric recurrent Markov process with state space S and let L-t(x) denote the local time of X at x is an element of S. For a fixed element 0 in the state space S, let tau (t) := inf{s: L-s(0) > t}. The 0-potential density, u({o})(x, y), of the process X killed at T-0 = inf{s: X-s = 0), is symmetric and positive definite. Let eta = {eta (x); x is an element of S} be a mean-zero Gaussian process with covariance E-eta(eta (x)eta (y)) = u({0})(x, y). The main result of this p...
-
作者：Liggett, TM
作者单位：University of California System; University of California Los Angeles
摘要：We consider a sequence of probability measures v(n) obtained by conditioning a random vector X = (X-1,... ,X-d) with nonnegative integer valued components on X-1 +(...)+ X-d = n - 1 and give several sufficient conditions on the distribution of X for v(n) to be stochastically increasing in n. The problem is motivated by an interacting particle system on the homogeneous tree in which each vertex has d + 1 neighbors. This system is a variant of the contact process and was studied recently by A. P...
