-
作者：NEWMAN, CM; PIZA, MST
作者单位：University of California System; University of California Irvine
摘要：We consider stochastic growth models, such as standard first-passage percolation on Z(d), where to leading order there is a linearly growing deterministic shape. Under natural hypotheses, we prove that for d = 2, the shape fluctuations grow at least logarithmically in all directions. Although this bound is far from the expected power law behavior with exponent chi = 1/3, it does prove divergence. With additional hypotheses, we obtain inequalities involving chi and the related exponent xi (whic...
-
作者：RIO, E
摘要：Let (X(i))(i is an element of Z) be a strictly stationary and strongly mixing sequence of real-valued mean zero random variables. Let (alpha(n))(n>0) be the sequence of strong mixing coefficients. We define the strong mixing fraction alpha (.) by alpha(t) = alpha([t]) and we denote by Q the quantile function of \X(0)\. Assume that (*) integral(0)(1) alpha(-1)(t)Q(2)(t)dt < infinity, where f(-1) denotes the inverse of the monotonic function f. The main result of this paper is that the functiona...
-
作者：ROSINSKI, J
摘要：A connection between structural studies of stationary non-Gaussian stable processes and the ergodic theory of nonsingular flows is established and exploited. Using this connection, a unique decomposition of a stationary stable process into three independent stationary parts is obtained. It is shown that the dissipative part of a flow generates a mixed moving average part of a stationary stable process, while the identity part of a flow essentially gives the harmonizable part. The third part of...
-
作者：DJEHICHE, B; KAJ, I
作者单位：Uppsala University
摘要：A principle of large deviations from the McKean-Vlasov Limit is derived for a class of measure-valued jump processes. It is shown that the associated rate function admits several representations, including the one obtained by entropy methods and the one derived by a pathwise approach.
-
作者：ALABERT, A; FERRANTE, M; NUALART, D
作者单位：University of Padua; University of Barcelona
摘要：The purpose of this paper is to prove a characterization of the conditional independence of two independent random Variables given a particular functional of them, in terms of a factorization property. As an application we discuss the Markov field property for solutions of stochastic differential equations with a boundary condition involving the values of the process at times t = 0 and t = 1.
-
作者：LYONS, R; PEMANTLE, R; PERES, Y
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
摘要：The Kesten-Stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process, shelving that an L log L condition is decisive. In critical and subcritical cases, results of Kolmogorov and later authors give the rate of decay of the probability that the process survives at least n generations. We give conceptual proofs of these theorems based on comparisons of Galton-Watson measure to another measure on the space of trees. This approach also explains Yaglom's ...
-
作者：LEDRAPPIER, F
摘要：We prove a central limit theorem for the distance of the Brownian point on the universal cover of a compact negatively curved Riemannian manifold. The technical point is a contraction property for the leafwise Brownian motion along the stable foliation.
-
作者：LEE, TY
摘要：For a system of infinitely many independent symmetric random walks on Z let K-n(x) be the number of visits to x is an element of Z from time 0 to n - 1. The probabilities of some rare events involving (K-n(0), K-n(1)) are estimated as n-->infinity and the corresponding large deviation rate functions are derived for both deterministic and invariant initial distributions. The dependence on the initial distributions is discussed. A simple method is used for guessing at the rate functions. This me...
-
作者：ANTAL, P
摘要：We consider a continuous time simple random walk moving among obstacles, which are sites (resp., bonds) of the lattice Z(d). We derive in this context a version of the technique of enlargement of obstacles developed by Sznitman in the Brownian case. This method gives controls on exponential moments of certain death times as well as good lower bounds for certain principal eigenvalues. We give an application to recover an asymptotic result of Donsker and Varadhan on the number of sites visited b...
-
作者：PEMANTLE, R; PERES, Y
作者单位：University of California System; University of California Berkeley
摘要：Evans defined a notion of what it means for a set B to be polar for a process indexed by a tree. The main result herein is that a tree picked from a Galton-Watson measure whose offspring distribution has mean m and finite variance will almost surely have precisely the same polar sets as a deterministic tree of the same growth rate. This implies that deterministic and nondeterministic trees behave identically in a variety of probability models. Mapping subsets of Euclidean space to trees and po...
