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作者：Brossard, J; Leuridan, C
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
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作者：Bertoin, J
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the age processes A((1)) greater than or equal to ... greater than or equal to A((n)) associated to a monotone sequence R-(1) subset of or equal to ... subset of or equal to R-(n) of regenerative sets. We obtain limit theorems in distribution for (A(t)((1)),...,A(t)((n))) and for ((1/t)A(t)((1)),..., (1/t)A(t)((n))), which correspond to multivariate versions of the renewal theorem and of the Dynkin-Lamperti theorem, respectively. Dirichlet distributions play a key role in the latter.
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作者：Groeneboom, P; Jongbloed, G; Wellner, JA
作者单位：Delft University of Technology; Vrije Universiteit Amsterdam; University of Washington; University of Washington Seattle
摘要：We study the two-dimensional process of integrated Brownian motion and Brownian motion, where integrated Brownian motion is conditioned to be positive. The transition density of this process is derived from the asymptotic behavior of hitting times of the unconditioned process. Explicit expressions for the transition density in terms of confluent hypergeometric functions are derived, and it is shown how our results on the hitting time distributions imply previous results of Isozaki-Watanabe and...
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作者：Dermoune, A
作者单位：Universite de Lille
摘要：This work presents a construction of a solution for the nonlinear stochastic differential equation X-t= X-0 + integral(0)(t)E[u(0)(X-0)\ X-s] ds, t greater than or equal to 0. The random variable X-0 with values in R and the function u(0) are given. We denote by P-t the probability distribution of X-t and u(x, t) = E[u(0)(X-0)\ X-t = x]. We prove that (P-t, u(., t), t greater than or equal to 0) is a weak solution for a system of conservation laws arising in adhesion particle dynamics.
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作者：Khoshnevisan, D; Shi, Z
作者单位：Utah System of Higher Education; University of Utah; Sorbonne Universite
摘要：The main goal of this paper is to present an explicit capacity estimate for hitting probabilities of the Brownian sheet. As applications, we determine the escape rates of the Brownian sheet and also obtain a local intersection equivalence between the Brownian sheet and the additive Brownian motion. Other applications concern quasi-sure properties in Wiener space.
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作者：Pemantle, R; Volkov, S
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：A stochastic process called vertex-reinforced random walk (VRRW) is defined in Pemantle [Ann. Probab. 16 1229-1241]. We consider this process in the case where the underlying graph is an infinite chain (i.e., the one-dimensional integer lattice). We show that the range is almost surely finite, that at least five points are visited infinitely often almost surely and that with positive probability the range contains exactly five points. There are always points visited infinitely often but at a s...
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作者：Delmas, JF
作者单位：Institut Polytechnique de Paris; Ecole des Ponts ParisTech
摘要：We first consider a super Brownian motion X with a general branching mechanism. Using the Brownian snake representation with subordination, we get the Hausdorff dimension of supp X-t, the topological support of X-t and, more generally, the Hausdorff dimension of U-t is an element of B supp X-t. We also provide estimations on the hitting probability of small balls for those random measures. We then deduce that the support is totally disconnected in high dimension. Eventually, considering a supe...
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作者：Benjamini, I; Lyons, R; Peres, Y; Schramm, O
作者单位：Weizmann Institute of Science; Hebrew University of Jerusalem; University of California System; University of California Berkeley; Indiana University System; Indiana University Bloomington
摘要：We show that independent percolation on any Cayley graph of a nonamenable group has no infinite components at the critical parameter. This result was obtained by the present authors earlier as a corollary of a general study of group-invariant percolation. The goal here is to present a simpler self-contained proof that easily extends to quasi-transitive graphs with a unimodular automorphism group. The key tool is a mass-transport method, which is a technique of averaging in nonamenable settings.
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作者：Hsing, T
作者单位：National University of Singapore; Texas A&M University System; Texas A&M University College Station
摘要：This paper investigates the asymptotic distribution of the partial sum S-N = Sigma(n=1)(N)[K(X-n) - EK(X-n)], as N --> infinity, where {X-n} is a moving average stable process and K is a bounded and measurable function. The results show that SN follows a central or non-central limit theorem depending on the rate at which the moving average coefficients tend to 0.
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作者：Bai, ZD; Silverstein, JW
作者单位：National University of Singapore; North Carolina State University
摘要：Let B-n = (1/N)T-n(1/2) X-n (XnTn1/2)-T-* where X-n is n x N with i.i.d. complex standardized entries having finite fourth moment, and T-n(1/2) is a Hermitian square root of the nonnegative definite Hermitian matrix T-n. It was shown in an earlier paper by the authors that, under certain conditions on the eigenvalues of T-n, with probability 1 no eigenvalues lie in any interval which is outside the support of the limiting empirical distribution (known to exist) for all large rt. For these n th...
