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作者：Carmona, P
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Brownian motion in a random Levy potential V is the informal solution of the stochastic differential equation dX(t) = dB(t) - 1/2V' (X-t) dt, where B is a Brownian motion independent of V. We generalize some results of Kawazu-Tanaka, who considered for V a Brownian motion with drift, by proving that X-t/t converges almost surely to a constant, the mean velocity, which we compute in terms of the Levy exponent phi of V, defined by E[e(mV(t))] = e(-t phi(m)).
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作者：Deheuvels, P
作者单位：Sorbonne Universite
摘要：We show that increments of size h(n) from the uniform quantile and uniform empirical processes in the neighborhood of a fixed point t(0) is an element of (0, 1) may have different rates of almost sure convergence to 0 in the range where h(n) --> 0 and nh(n)/log n --> infinity. In particular, when h(n) + n(-lambda) with 0 < lambda < 1, we obtain that these rates are identical for 1/2 < lambda < 1, and distinct for 0 < lambda < 1/2. This phenomenon is shown to be a consequence of functional laws...
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作者：Salzano, M; Schonmann, RH
作者单位：University of California System; University of California Los Angeles
摘要：We study the ergodic behavior of the contact process on infinite connected graphs of bounded degree. We show that the fundamental notion of complete convergence is not as well behaved as it was thought to be. In particular there are graphs for which complete convergence holds in any number of separated intervals of values of the infection parameter and fails for the other values of this parameter. We then introduce a basic invariant probability measure related to the recurrence properties of t...
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作者：Lachal, A
作者单位：Universite Claude Bernard Lyon 1
摘要：Let (B(t))(t greater than or equal to 0) be the linear Brownian motion starting at 0, and set X-n(t) = (1/n!) integral(0)(t)(t - s)(n) dB(s). Watanabe stated a law of the iterated logarithm for the process (X-1(t))(t greater than or equal to 0), among other things, This paper proposes an elementary proof of this fact, which can be extended to the general case n greater than or equal to 1. Next, we study the local asymptotic classes (upper and lower) of the (n + 1)-dimensional process U-n = (B,...
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作者：Takanobu, S
作者单位：Kanazawa University
摘要：The error estimate of the integral kernel for the Trotter product formula for Schrodinger operators is shown. A basic tool for doing so is the Feynman-Kac formula based on the pinned Brownian motion. This formula enables us to express the integral kernel in handleable form and hence estimate it. As a consequence the Trotter product formula in the L-p operator norm is obtained.
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作者：Hennion, H
作者单位：Universite de Rennes
摘要：Let S be the set of q x q matrices with positive entries, such that each column and each row contains a strictly positive element, and denote by S degrees the subset of these matrices, all entries of which are strictly positive. Consider a random ergodic sequence (X-n)(n greater than or equal to 1) in S. The aim of this paper is to describe the asymptotic behavior of the random products X-(n) = X-n... X-1, n greater than or equal to 1, under the main hypothesis P(U)(n greater than or equal to ...
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作者：De La Pena, VH; Lai, TL
作者单位：Columbia University; Stanford University
摘要：In this paper we provide sharp bounds on the L-p-norms of randomly stopped U-statistics. These bounds consist mainly of decoupling inequalities designed to reduce the level of dependence between the U-statistics and the stopping time involved. we apply our results to obtain Wald's equation for U-statistics, moment convergence theorems and asymptotic expansions for the moments of randomly stopped U-statistics. The proofs are based an decoupling inequalities, symmetrization techniques, the use o...
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作者：Fleming, WH; Sheu, SJ
作者单位：Brown University; Academia Sinica - Taiwan
摘要：The asymptotic behaviors of the principal eigenvalue and the corresponding normalized eigenfunction of the operator G(epsilon) f = (epsilon/2)Delta f + g del f + (l/epsilon)f for Small epsilon are studied. Under some conditions, the first order expansions for them are obtained. Two applications to risk-sensitive control problems are also mentioned.
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作者：Newman, CM; Wu, CC
作者单位：New York University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University
摘要：We consider inhomogeneous nearest neighbor Bernoulli bond percolation on Z(d) where the bonds in a fixed s-dimensional hyperplane (1 less than or equal to s less than or equal to d - 1) have density p(1) and all other bonds have fixed density, p(c)(Z(d)), the homogeneous percolation critical value. For s greater than or equal to 2, it is natural to conjecture that there is a new critical value, p(c)(s)(Z(d)), for p(1), strictly between p(c)(Z(d)) and p(c)(Z(s)); we prove this for large d and 2...
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作者：Povel, T
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We derive a large deviation principle for the position at large times t of a one-dimensional annealed Brownian motion in a Poissonian potential in the critical spatial scale t(1/3). Here annealed means that averages are taken with respect to both the path and environment measures. In contrast to the d-dimensional case for d greater than or equal to 2 in. the critical scale t(d/(d + 2)) as treated by Sznitman, the rate function which measures the large deviations exhibits three different regime...
