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作者：Sethuraman, S
作者单位：Iowa State University; University of Minnesota System; University of Minnesota Twin Cities
摘要：Some invariance principles for additive functionals of simple exclusion with finite-range translation-invariant jump rates p(i, j) = p(j - i) in dimensions d greater than or equal to 1 are established. A previous investigation concentrated on the case of p symmetric. The principal tools to take care of nonreversibility, when p is asymmetric, are invariance principles for associated random variables and a local balance estimate on the asymmetric generator of the process. As a by-product, we pro...
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作者：Higuchi, Y; Zhang, Y
作者单位：Kobe University; University of Colorado System; University of Colorado at Colorado Springs
摘要：Consider first passage Ising percolation on Z(2). Let beta denote the reciprocal temperature and let h denote an external magnetic field. Denote by beta(c) the critical temperature and, for beta < beta(c), let h(c)(beta)= h(c) = sup{h: theta(beta, h) = 0}, where theta(beta, h) is the probability that the origin is connected by an infinite (+)-cluster. With these definitions let us consider first passage Ising percolation on Z(2). Let a(0,n) denote the first passage time from (0, 0) to (n, 9). ...
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作者：Van den Berg, J; Kesten, H
作者单位：Cornell University
摘要：We consider a system of particles, each of which performs a continuous time random walk on Z(d). The particles interact only at times when a particle jumps to a site at which there are a number of other particles present. If there are j particles present, then the particle which just jumped is removed from the system with probability p(j). We show that if p(j) is increasing in j and if the dimension d is at least 6 and if we start with one particle at each site of Z(d), then p(t) := P{there is...
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作者：Surgailis, D
作者单位：Vilnius University
摘要：We study limit distributions of sums S-N((G)) = Sigma(t=1)(N) G(X-t) of nonlinear functions G(x) in stationary variables of the form X-t = Y-t + Z(t), where {Y-t} is a linear (moving average) sequence with long-range dependence, and {Z(t)} is a (nonlinear) weakly dependent sequence. In particular, we consider the case when {Y-t} is Gaussian and either (1) {Z(t)} is a weakly dependent multilinear form in Gaussian innovations, or (2) {Z(t)} is a finitely dependent functional in Gaussian innovati...
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作者：Mikulevicius, R
作者单位：Vilnius University
摘要：We study Cauchy's problem for certain second-order linear parabolic stochastic differential equation (SPDE) driven by a cylindrical Brownian motion. Considering its solution as a function with values in a probability space and using the methods of deterministic partial differential equations, we establish the existence and uniqueness of a strong solution in Holder classes.
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作者：Applebaum, D; Estrade, A
作者单位：Nottingham Trent University; Universite de Orleans
摘要：Under a natural invariance assumption on the Levy measure we construct compound Poisson processes and more general isotropic Levy processes on Riemannian manifolds by projection of a suitable horizontal process in the bundle of orthonormal frames. We characterize such Levy processes through their infinitesimal generators and we show that they can be realized as the limit of a sequence of Brownian motions which are interlaced with jumps along geodesic segments.
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作者：Erickson, KB
作者单位：University of Washington; University of Washington Seattle
摘要：Given any closed subset C of (R-d)overbar, containing a pair of antipodal points at oo, there is a sequence of independent and identically distributed random variables {X-i} such that the set of limit points (in the topology of (R-d)overbar) of {(X-1 +...+X-t)/t}(t greater than or equal to 1) equals C. Here (R-d) is the compact space gotten by adjoining the sphere, S(d-1)infinity at infinity.
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作者：Virág, B
作者单位：University of California System; University of California Berkeley
摘要：Lyons, Pemantle and Peres asked whether the asymptotic lower speed in an infinite tree is bounded by the asymptotic speed in the regular tree with the same average number of branches. In the more general setting of random walks on graphs, we establish a bound on the expected value of the exit time from a vertex set in terms of the size and distance from the origin of its boundary, and prove this conjecture. We give sharp bounds for limiting speed (or, when applicable, sublinear rate of escape)...
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作者：Blount, D; Bose, A
作者单位：Arizona State University; Arizona State University-Tempe; Carleton University
摘要：The superprocess and its occupation time process are represented as Hilbert space valued solutions of stochastic evolution equations by using the Fourier transform of the process. For appropriate parameter values, the existence of density valued solutions follows. Pathwise regularity of the processes is obtained. As a new tool we develop a maximal inequality. We also extend the Tanaka-like evolution equations developed for local time processes and provide an Ito formula for certain functionals...
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作者：Chen, MF; Wang, FY
作者单位：Beijing Normal University
摘要：In this paper, some new forms of Cheeger's inequalities are established for general (maybe unbounded) symmetric forms (Theorems 1.1 and 1.2): the resulting estimates improve and extend the ones obtained by Lawler and Sokal for bounded jump processes. Furthermore, some existence criteria for spectral gap of general symmetric forms or general reversible Markov processes are presented (Theorems 1.4 and 3.1), based on Cheeger's inequalities and a relationship between the spectral gap and the first...
