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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...
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作者：Wieand, K
作者单位：University of Arizona
摘要：Let M be a randomly chosen n x n permutation matrix. For a fixed are of the unit circle, let X be the number of eigenvalues of M which lie in the specified are. We calculate the large n asymptotics for the mean and variance of X, and show that (X - E[X])/(Var(X))(1/2) is asymptotically normally distributed. In addition, we show that for several fixed arcs I-1,...,I-m, the corresponding random variables are jointly normal in the large n limit.
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作者：Gut, A; Spataru, A
作者单位：Uppsala University; Romanian Academy; Institute of Mathematical Statistics & Applied Mathematics of Romanian Academy
摘要：Let X, X-1, X-2,... be i.i.d. random variables with mean 0 and positive, finite variance sigma (2), and set S-n = X-1 + ... + X-n, n greater than or equal to 1. Continuing earlier work related to strong laws, we prove the following analogs for the law of the iterated logarithm: lim(epsilon down arrow sigma root2) root epsilon (2)-2 sigma (2) Sigma (n greater than or equal to3) 1/n P(\S-n\ greater than or equal to epsilon rootn log log n + a(n)) = sigma root2 whenever a(n) = O(rootn(log log n)(...
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作者：Rosinski, J
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：This work is concerned with the structural analysis of stationary alpha -stable random fields. Three distinct classes of such random fields are characterized and it is shown that every stationary alpha -stable random field can be uniquely decomposed into the sum of three independent components belonging to these classes. Various examples of stationary alpha -stable random fields are discussed in this context.
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作者：Talagrand, B
作者单位：Sorbonne Universite; University System of Ohio; Ohio State University
摘要：In a previous work, we proved the validity of the replica-symmetric solution for the Hopfield model in a nontrivial domain of parameters. This was done at the accuracy of the LLN. In a somewhat larger domain, we obtain a description at the level of the CLT, or, in the terminology of physics, we calculate the fluctuations around the mean field. This is obtained by refining the tools we developed for a rigorous use of the cavity method and proving new a priori estimates about the localization of...
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作者：Mueller, C
作者单位：University of Rochester
摘要：Consider the stochastic partial differential equation u(t) = u(xx) + u(gamma)(W)over dot, where x epsilon I equivalent to [0, J], (W)over dot = (W)over dot(t, x) is 2-parameter white noise, and we assume that the initial function u(0, x) is nonnegative and not identically 0. We impose Dirichlet boundary conditions on u in the interval I. We say that u blows up in finite time, with positive probability, if there is a random time T < infinity such that P(lim(t up arrowT) sup(x) u( t, x) = infini...
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作者：Cranston, M; Scheutzow, M; Steinsaltz, D
作者单位：University of Rochester; Technical University of Berlin
摘要：It has been suggested that stochastic flows might be used to model the spread of passive tracers in a turbulent fluid. We define a stochastic flow by the equations phi (0)(x) = x, d phi (t)(x) = F(dt, phi (t)(x)), where F(t, x) is a field of semimartingales on x is an element of R-d for d greater than or equal to 2 whose local characteristics are bounded and Lipschitz. The particles are points in a bounded set X, and we ask how far the substance has spread in a time T. That is, we define Phi (...
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作者：Cox, JT; Geiger, J
作者单位：Syracuse University; Goethe University Frankfurt
摘要：The genealogy of a cluster in the multitype voter model can be defined in terms of a family of dual coalescing random walks. We represent the genealogy of a cluster as a point process in a size-time plane and show that in high dimensions the genealogy of the cluster at the origin has a weak Poisson limit. The limiting point process is the same as for the genealogy of the size-biased Galton-Watson tree. Moreover, our results show that the branching mechanism and the spatial effects of the voter...
