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作者：Dembo, A
作者单位：Stanford University; Stanford University
摘要：We derive inequalities of the form Delta(P, Q) less than or equal to H(P\R) + H(Q\R) which hold for every choice of probability measures P, Q, R, where H(P\R) denotes the relative entropy of P with respect to R acid Delta(P, Q) stands for a coupling type distance between P and Q. Using the chain rule for relative entropies and then specializing to Q with a given support we recover some of Talagrand's concentration of measure inequalities for product spaces.
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作者：de Fitte, PR
作者单位：Universite de Rouen Normandie
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作者：Hamana, Y
作者单位：Kyushu University
摘要：We study the fluctuation problem for the multiple point range of random walks in the two dimensional integer lattice with mean 0 and finite variance. The p-multiple point range means the number of distinct sites with multiplicity p of random walk paths before time n. The suitably normalized multiple point range is proved to converge to a constant, which is independent of the multiplicity, multiple of the renormalized self-intersection local time of a planar Brownian motion.
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作者：Pitman, J; Yor, M
作者单位：University of California System; University of California Berkeley
摘要：The two-parameter Poisson-Dirichlet distribution, denoted PD(alpha, theta), is a probability distribution on the set of decreasing positive sequences with sum 1. The usual Poisson-Dirichlet distribution with a single parameter theta, introduced by King-man, is PD(0, theta). Known properties of PD(0, theta), including the Markov chain description due to Vershik, Shmidt and Ignatov, are generalized to the two-parameter case. The size-biased random permutation of PD(alpha, theta) is a simple resi...
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作者：Dynkin, EB; Kuznetsov, SE
作者单位：Cornell University; Russian Academy of Sciences
摘要：Suppose that E is an arbitrary domain in R-d, L is a second order elliptic differential operator in S = R+ x E and S-e is the extremal part of the Martin boundary for the corresponding diffusion xi. Let 1 < alpha less than or equal to 2. We investigate a boundary value problem partial derivative u/partial derivative r + Lu - u(alpha) = -eta inS, (*) u = v on S-e, u = 0 on {infinity} x E involving two measures eta and v. For the existence of a solution, we give sufficient conditions in terms of...
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作者：Föllmer, H; Gantert, N
作者单位：Humboldt University of Berlin; Technical University of Berlin
摘要：Schrodinger processes are defined as mixtures of Brownian bridges which preserve the Markov property. In finite dimensions, they can be characterized as h-transforms in the sense of Doob for some space-time harmonic function h of Brownian motion, and also as solutions to a large deviation problem introduced by Schrodinger which involves minimization of relative entropy with given marginals. As a basic case study in infinite dimensions, we investigate these different aspects for Schrodinger pro...
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作者：Chang, JT; Peres, Y
作者单位：Yale University; University of California System; University of California Berkeley; Hebrew University of Jerusalem
摘要：Let {S-n: n greater than or equal to 0} be a random walk having normally distributed increments with mean theta and variance 1, and let tau be the time at which the random walk first takes a positive value, so that S-tau is the first ladder height. Then the expected value EthetaStau, originally defined for positive theta, may be extended to be an analytic function of the complex variable theta throughout the entire complex plane, with the exception of certain branch point singularities. In par...
