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作者：Manstavicius, M
作者单位：University of Connecticut
摘要：Let xit, t is an element of [0, T], be a strong Markov process with values in a complete separable metric space (X, rho) and with transition probability function P-s,P-t (x, dy), 0 less than or equal to s less than or equal to t less than or equal to T, x is an element of X. For any h is an element of [0, T] and a > 0, consider the function alpha(h,a) = sup{P-s,P-t(x, {y:rho(x,y) greater than or equal to a}):x is an element of X, 0 less than or equal to s less than or equal to t less than or e...
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作者：Lijoi, A; Regazzini, E
作者单位：University of Pavia; University of Pavia
摘要：The Lauricella theory of multiple hypergeometric functions is used to shed some light on certain distributional properties of the mean of a Dirichlet process. This approach leads to several results, which are illustrated here. Among these are a new and more direct procedure for determining the exact form of the distribution of the mean, a correspondence between the distribution of the mean and the parameter of a Dirichlet process, a characterization of the family of Cauchy distributions as the...
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作者：Fleischmann, K; Swart, JM
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Erlangen Nuremberg
摘要：In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of continuous superprocesses with Feller underlying motion on compact spaces, we identify the trimmed tree, which turns out to be a binary splitting particle system with a new underlying motion that is a compensated h-transform of the old one. We show how trimmed trees may be estimated from above by embe...
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作者：Fuhrman, M; Tessitore, G
作者单位：Polytechnic University of Milan; University of Parma
摘要：Solutions of semilinear elliptic differential equations in infinite-dimensional spaces are obtained by means of forward and backward infinite-dimensional stochastic evolution equations. The backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition. Elliptic equations are intended in a mild sense, suitable also for applications to optimal control. We finally notice that, due to the lack of smoothing properties, the elliptic partial ...
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作者：Wu, JM
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Let X (t) be the symmetric alpha-stable process in R-d (0 < alpha < 2, d greater than or equal to 2). Then let W(f) be the thorn {x is an element of R-d:0 < x(1) < 1, (x(2)(2) +... + x(d)(2))(1)/(2) < f(x(1))} where f : (0, 1) --> (0, 1) is continuous, increasing with f (0(+)) = 0. Recently Burdzy and Kulczycki gave an exact integral condition on f for the existence of a random time s such that X(t) remains in the thorn X(s) + W(f) for all t is an element of [s, s + 1). We extend their theorem...
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作者：Bobkov, SG
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：For noncorrelated random variables, we study a concentration property of the family of distributions of normalized sums formed by sequences of times of a given large length.
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作者：Baudoin, F
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We extend to Riemannian manifolds the theory of conditioned stochastic differential equations. We also provide some enlargement formulas for the Brownian filtration in this nonflat setting.
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作者：Külske, C; Le Ny, A; Redig, F
作者单位：Technical University of Berlin; Universite Paris Saclay; Eindhoven University of Technology
摘要：We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of almost Gibbsian measures (almost sure continuity of conditional probabilities). For quasilocal measures, we obtain a full variational principle. For the joint measures of the random field Ising model, we show that the weak Gibbs property holds, with an almost surely rapidly decaying translation-invariant potent...
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作者：Lifshits, MA; Shi, Z
作者单位：Saint Petersburg State University; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Consider a simple symmetric random walk on the integer lattice Z. For each n, let V(n) denote a favorite site (or most visited site) of the random walk in the first n steps. A somewhat Surprising theorem of Bass and Griffin [Z. Wahrsch. Verw. Gebiete 70 (1985) 417-436] says that V is almost surely transient, thus disproving a previous conjecture of Erdos and Revesz [Mathematical Structures-Computational Mathematics-Mathematical Modeling 2 (1984) 152-157]. More precisely, Bass and Griffin prove...
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作者：Alon, N; Benjamini, I; Stacey, A
作者单位：Microsoft; Tel Aviv University; Tel Aviv University; University of Cambridge
摘要：Consider a uniform expanders family G(n) with a uniform bound on the degrees. It is shown that for any p and c > 0, a random subgraph of G(n) obtained by retaining each edge, randomly and independently, with probability p, will have at most one cluster of size at least c\G(n)\, with probability going to one, uniformly in p. The method from Ajtai, Komlos and Szemeredi [Combinatorica 2 (1982) 1-7] is applied to obtain some new results about the critical probability for the emergence of a giant c...
