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作者：Gantert, N
作者单位：Technical University of Berlin
摘要：We consider an infinite Galton-Watson tree Gamma and label the vertices nu with a collection of i.i.d. random variables (Y-nu)(nu is an element of Gamma). In the case where the upper tail of the distribution of Y-nu is semiexponential, we then determine the speed of the corresponding tree-indexed random walk. In contrast to the classical case where the random variables Y-nu have finite exponential moments, the normalization in the definition of the speed depends on the distribution of Y-nu. In...
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作者：Hug, D; Last, G
作者单位：University of Freiburg; Helmholtz Association; Karlsruhe Institute of Technology
摘要：This paper is concerned with contact distribution functions of a random closed set Xi = U(n=1)(infinity) Xi (n) in R(d), where the Xi (n) are assumed to be random nonempty convex bodies. These distribution functions are defined here in terms of a distance function which is associated with a strictly convex gauge body (structuring element) that contains the origin in its interior. Support measures with respect to such distances will be introduced and extended to sets in the local convex ring. T...
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作者：Blount, D; Bose, A
作者单位：Arizona State University; Arizona State University-Tempe; Carleton University
摘要：The superprocess and its occupation time process are represented as Hilbert space valued solutions of stochastic evolution equations by using the Fourier transform of the process. For appropriate parameter values, the existence of density valued solutions follows. Pathwise regularity of the processes is obtained. As a new tool we develop a maximal inequality. We also extend the Tanaka-like evolution equations developed for local time processes and provide an Ito formula for certain functionals...
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作者：Eisenbaum, N; Kaspi, H; Marcus, MB; Rosen, J; Shi, Z
作者单位：Sorbonne Universite; City University of New York (CUNY) System; City College of New York (CUNY); Technion Israel Institute of Technology; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：Let X be a strongly symmetric recurrent Markov process with state space S and let L-t(x) denote the local time of X at x is an element of S. For a fixed element 0 in the state space S, let tau (t) := inf{s: L-s(0) > t}. The 0-potential density, u({o})(x, y), of the process X killed at T-0 = inf{s: X-s = 0), is symmetric and positive definite. Let eta = {eta (x); x is an element of S} be a mean-zero Gaussian process with covariance E-eta(eta (x)eta (y)) = u({0})(x, y). The main result of this p...
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作者：Kuelbs, J
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：The existence of a dominating point for an open convex set and a corresponding representation formula for large deviation probabilities are established in the infinite-dimensional setting under conditions which are both necessary and sufficient and follow from those used previously in R-d. A precise nonlogarithmic estimate of large deviation probabilities applicable to Gaussian measures is also included.
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作者：Letac, G; Wesolowski, J
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Warsaw University of Technology; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Warsaw
摘要：Matsumoto and Yor have recently discovered an interesting transformation which preserves a bivariate probability measure which is a product of the generalized inverse Gaussian (GIG) and gamma distributions. This paper is devoted to a detailed study of this phenomenon. Let X and Y be two independent positive random variables. We prove (Theorem 4.1) that U = (X + Y)(-1) and V = X-1 - (X + Y)(-1) are independent if and only if there exists p, a, b > 0 such that Y is gamma distributed with shape p...
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作者：Liggett, TM
作者单位：University of California System; University of California Los Angeles
摘要：We consider a sequence of probability measures v(n) obtained by conditioning a random vector X = (X-1,... ,X-d) with nonnegative integer valued components on X-1 +(...)+ X-d = n - 1 and give several sufficient conditions on the distribution of X for v(n) to be stochastically increasing in n. The problem is motivated by an interacting particle system on the homogeneous tree in which each vertex has d + 1 neighbors. This system is a variant of the contact process and was studied recently by A. P...
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作者：Zhang, TS
作者单位：University of Manchester
摘要：In this paper, we establish a small time large deviation principle and obtain the following small time asymptotics: lim(t-->0) 2t log P(X-0 is an element of B, X-t is an element of C) = -d(2)(B, C), for diffusion processes on Hilbert spaces, where d(B, C) is the intrinsic metric between two subsets B and C associated with the diffusions. The case of perturbed Ornstein-Uhlenbeck processes is treated separately at the end of the paper.
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作者：Albeverio, S; Zhao, XL
作者单位：University of Bonn; Fudan University
摘要：Measure-valued branching random walks (superprocesses) on p-adics are introduced and investigated. The uniqueness and existence of solutions to associated linear and nonlinear heat-type (parabolic) equations are proved, provided some condition on the parameter of the random walks is satisfied. The solutions of these equations are shown to be locally constant if their initial values are. Moreover, the heat-type equations can be identified with a system of ordinary differential equations. Condit...
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作者：Mikosch, T; Samorodnitsky, G
作者单位：University of Groningen; Cornell University; Cornell University
摘要：For a random walk with negative drift we study the exceedance probability (ruin probability) of a high threshold. The steps of this walk (claim sizes) constitute a stationary ergodic stable process. We study how ruin occurs in this situation and evaluate the asymptotic behavior of the ruin probability for a large variety of stationary ergodic stable processes. Our findings show that the order of magnitude of the ruin probability varies significantly from one model to another. In particular, ru...
