作者：Einmahl, Uwe; Kuelbs, Jim
作者单位：Vrije Universiteit Brussel; University of Wisconsin System; University of Wisconsin Madison
摘要：Let X, X-1, X-2,... be i.i.d, mean zero random vectors with values in a separable Banach space B, S-n = X-1 +...+ X-n for n >= 1, and assume {c(n) : n >= 1} is a suitably regular sequence of constants. Furthermore, let S((n)) (t), 0 <= t <= 1 be the corresponding linearly interpolated partial sum processes. We study the cluster sets A = C({S-n/c(n)}) and A = C({S((n))(.)/c(n)}). In particular, A and A are shown to be nonrandom, and we derive criteria when elements in B and continuous functions...
作者：Wang, Feng-Yu
作者单位：Beijing Normal University; Swansea University
摘要：A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move together as soon as possible, for the new-type coupling the two marginal processes start from the same point but their difference is aimed to reach a fixed quantity at a given time. Besides the integration by parts formula, the new coupling method is also efficient...
作者：Cerf, Raphael; Theret, Marie
作者单位：Universite Paris Saclay; Universite Paris Saclay; Universite Paris Cite
摘要：We consider the standard first passage percolation model in the resealed graph Z(d)/n for d >= 2 and a domain Omega of boundary Gamma in R-d Let Gamma(1) and Gamma(2) be two disjoint open subsets of Gamma, representing the parts of Gamma through which some water can enter and escape from Omega. A law of large numbers for the maximal flow from Gamma(1), to Gamma(2) in Omega is already known. In this paper we investigate the asymptotic behavior of a maximal stream and a minimal cutset. A maximal...
