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作者：Pisztora, A; Povel, T; Zeitouni, O
作者单位：Harvard University; Massachusetts Institute of Technology (MIT); Technion Israel Institute of Technology
摘要：Suppose that the integers are assigned i.i.d. random variables {w(x)} (taking values in the interval [1/2, 1)), which serve as an environment. This environment defines a random walk {X-k} (called a RWRE) which, when at x, moves one step to the right with probability omega(x), and one step to the left with probability 1 - omega(x). Solomon (1975) determined the almost-sure asymptotic speed (= rate of escape) of a RWRE, in a more general set-up. Dembo, Peres and Zeitouni (1996), following earlie...
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作者：Pardoux, E; Tang, SJ
作者单位：Aix-Marseille Universite; Fudan University
摘要：This paper studies, under some natural monotonicity conditions, the theory (existence and uniqueness, a priori estimate, continuous dependence on a parameter) of forward-backward stochastic differential equations and their connection with quasilinear parabolic partial differential equations. We use a purely probabilistic approach, and allow the forward equation to be degenerate.
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作者：Wentzell, AD
作者单位：Tulane University
摘要：For a certain class of families of stochastic processes eta(epsilon)(t), 0 less than or equal to t less than or equal to T, constructed starting from sums of independent random variables, limit theorems for expectations of functionals F(eta(epsilon)[0, T]) are proved of the form EF(eta(epsilon)[0, T]) = E[F(omega(0)[0,T]) + (i=1)Sigma(m) epsilon(j/2) . A(i)F(omega(0)[0,T])] + o(epsilon(m/2)) (epsilon down arrow 0), where omega(0) is a Wiener process starting from 0, with variance sigma(2) per ...
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作者：Häggström, O; Peres, Y
作者单位：Chalmers University of Technology; University of California System; University of California Berkeley; Hebrew University of Jerusalem
摘要：Consider site or bond percolation with retention parameter p on an infinite Cayley graph. In response to questions raised by Grimmett and Newman (1990) and Benjamini and Schramm (1996), we show that the property of having (almost surely) a unique infinite open cluster is increasing in p. Moreover, in the standard coupling of the percolation models for all parameters, a.s. for all p(2) > p(1) > p(c), each infinite p(2)-cluster contains an infinite pr-cluster; this yields an extension of Alexand...
