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作者：Shao, QM
作者单位：University of Oregon
摘要：Let {X, X-n, n greater than or equal to 1} be a sequence of independent and identically distributed random variables. The classical Cramer-Chernoff large deviation states that lim(n-->infinity) n(-1) ln P((Sigma(i=1)(n) X-i)/n greater than or equal to x) = ln rho(x) if and only if the moment generating function of X is finite in a right neighborhood of zero. This paper uses n((p-1)/p)V(n,p) = n((p-1)/p)(Sigma(i=1)(n) \X-i\(p))(1/p) (p > 1) as the normalizing constant to establish a self-normal...
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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：Klass, MJ; Nowicki, K
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Lund University
摘要：Let X-1, Y-1, Y-2,..., X-n, Y-n be independent nonnegative rv's and let {b(ij)}(1 less than or equal to i, j less than or equal to n) be an array of nonnegative constants. We present a method of obtaining the order of magnitude of E Phi (Sigma(1 less than or equal to i, j less than or equal to n) b(ij) X-i Y-j), for any such {X-i}, {Y-i} and {b(ij)} and any nondecreasing function Phi on [0, infinity) with Phi(0) = 0 and satisfying a Delta(2) growth condition Furthermore, this technique is exte...
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作者：Alexander, KS
作者单位：University of Southern California
摘要：For a nonnegative subadditive function h on Z(d), with limiting approximation g(x) = lim(n) h(nx)/n, it is of interest to obtain bounds on the discrepancy between g(x) and h(x), typically of order \x\(nu) with nu < 1. For certain subadditive h(x), particularly those which are expectations associated with optimal random paths from 0 to x, in a somewhat standardized way a more natural and seemingly weaker property can be established: every x is in a bounded multiple of the convex hull of the set...
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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：Hambly, BM
作者单位：University of Edinburgh
摘要：We introduce a random recursive fractal based on the Sierpinski gasket and construct a diffusion upon the fractal via a Dirichlet form. This form and its symmetrizing measure are determined by the electrical resistance of the fractal. The effective resistance provides a metric with which to discuss the properties of the fractal and the diffusion. The main result is to obtain uniform upper and lower bounds for the transition density of the Brownian motion on the fractal in terms of this metric....
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作者：Dynkin, EB; Kuznetsov, SE
作者单位：Russian Academy of Sciences; Central Economics & Mathematics Institute RAS
摘要：We investigate natural linear additive (NLA) functionals of a general critical (xi, K, psi)-superprocess X. We prove that all of them have only fixed discontinuities. All homogeneous NLA functionals of time-homogeneous superprocesses are continuous (this was known before only in the case of quadratic branching). We introduce an operator epsilon(u) defined in terms of (xi, K, psi) and we prove that the potential h and the log-potential u of a NLA functional A are connected by the equation u + e...
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作者：Bunge, J
作者单位：Cornell University
摘要：A random variable X is C-decomposable if X = (D) cX + Y-c for all c in C, where Y-c is a random variable independent of X and C is a closed multiplicative subsemigroup of [0, 1]. X is self-decomposable if C = [0, 1]. Extending an idea of Urbanik in the self-decomposable case, we define a decreasing sequence of subclasses of the class of C-decomposable laws, for any C. We give a structural representation for laws in these classes, and we show that laws in the limiting subclass are infinitely di...
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作者：Grama, IG
作者单位：Academy of Sciences of Moldova
摘要：Let X-n = (X-t(n), F-t(n))(0 less than or equal to t less than or equal to 1) be square integrable martingales with the quadratic characteristics [X-n], n = 1, 2, .... We prove that the large deviations relation P(X-1(n) greater than or equal to r)/(1 - Phi(r)) --> 1 holds true for r growing to infinity with some rate depending on L-2 delta(n) = E Sigma(0 less than or equal to t less than or equal to 1) \Delta X-t(n)\(2+2 delta) and N-2 delta(n) = E\[X-n](1) - 1\(1+delta), where delta > 0 and ...
