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作者：Sznithman, AS
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We introduce in this article a class of transient random walks in a random environment on Z(d). When d greater than or equal to 2, these walks are ballistic and we derive a law of large numbers, a central limit theorem and large-deviation estimates. In the so-called nestling situation, large deviations in the neighborhood of the segment [0, v], v being the limiting velocity, are critical. They are of special interest in view of their close connection with the presence of traps in the medium, t...
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作者：Alòs, E; Mazet, O; Nualart, D
作者单位：Autonomous University of Barcelona; University of Barcelona
摘要：In this paper we develop a stochastic calculus with respect to a Gaussian process of the form B-t = integral (t)(0) K(t, s) dW(s), where W is a Wiener process and K(t, s) is a square integrable kernel, using the techniques of the stochastic calculus of variations. We deduce change-of-variable formulas for the indefinite integrals and we study the approximation by Riemann sums. The particular case of the fractional Brownian motion is discussed.
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作者：Biskup, M; König, W
作者单位：Microsoft; Technical University of Berlin
摘要：We consider the parabolic Anderson problem partial derivative (t)u = kappa Deltau + xiu on (0, infinity) x Z(d) with random i.i.d. potential xi = (xi (z))(z is an element ofZ)(d) and the initial condition u(0, (.)) equivalent to 1. Our main assumption is that esssup xi (0) = 0. Depending on the thickness of the distribution Prob( xi (0) is an element of (.)) close to its essential supremum, we identify both the asymptotics of the moments of u(t, 0) and the almost-sure asymptotics of u(t, 0) as...
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作者：Schlather, M
作者单位：Lancaster University
摘要：This paper aims to combine the central limit theorem with the limit theorems in extreme value theory through a parametrized class of limit theorems where the former ones appear as special cases. To this end the limit distributions of suitably centered and normalized l(cp(n))-norms of n-vectors of positive i.i.d. random variables are investigated. Here, c is a positive constant and p(n) is a sequence of positive numbers that is given intrinsically by the form of the upper tail behavior of the r...
