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作者：Ledoux, M; Lyons, T; Qian, Z
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Oxford
摘要：The goal of this paper is to construct canonical Levy area processes for Banach space valued Brownian motions via dyadic approximations. The significance of the existence of canonical Levy area processes is that a (stochastic) integration theory can be established for such Brownian motions (in Banach spaces). Existence of flows for stochastic differential equations with infinite dimensional noise then follows via the results of Lyons and Lyons and Qian [see, e.g., System Control and Rough Path...
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作者：Athreya, KB; Dai, JJ
作者单位：Iowa State University
摘要：Let {X-n}(0)(infinity) be a Markov chain with values in [0, 1] generated by the iteration of random logistic maps defined by Xn+1 = f(Cn+1) (X-n) equivalent to Cn+1 X-n (1 - X-n), n = 0, 1, 2,..., with {C-n}(1)(infinity) being independent and identically distributed random variables with values in [0, 4] and independent of X-0. This paper provides a class of examples where C-i take only two values lambda and mu such that there exist two distinct invariant probability distributions pi(0) and pi...
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作者：Soshnikov, A
作者单位：University of California System; University of California Davis
摘要：We prove that, under fairly general conditions, a properly rescaled determinantal random point field converges to a generalized Gaussian random process.
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作者：Asselah, A; Ferrari, PA
作者单位：Aix-Marseille Universite; Universidade de Sao Paulo
摘要：We consider the symmetric simple exclusion process on Z(d) for d greater than or equal to 5, and study the regularity of the quasi-stationary measures of the dynamics conditioned on not occupying the origin. For each rho is an element of]0, 1[, we establish uniqueness of the density of quasi-stationary measures in L-2(d(upsilonrho)), where upsilon(rho) is the stationary measure of density p. This, in turn, permits us to obtain sharp estimates for P-upsilonrho(tau > t), where tau is the first t...
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作者：Bercu, B; Gassiat, E; Rio, E
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the supremum W-n of self-normalized empirical processes indexed by unbounded classes of functions F. Such variables are of interest in various statistical applications, for example, the likelihood ratio tests of contamination. Using the Herbst method, we prove an exponential concentration inequality for W-n under a second moment assumption on the envelope function of F. This inequality is applied to obtain moderate deviations for W-n. We also provide large deviations results for so...
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作者：Häggström, O; Jonasson, J; Lyons, R
作者单位：University of Gothenburg; Indiana University System; Indiana University Bloomington; Chalmers University of Technology
摘要：The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models. In this paper, several new results are obtained for the random-cluster model on nonamenable graphs with cluster parameter q greater than or equal to 1. Among these, the main ones are the absence of percolation for the free random-cluster measure at the critical value and examples of planar regular graphs with regular dual where p(c)(free)(q) > p(u)(wired)(q) for q large enoug...
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作者：Tolmatz, L
摘要：Smirnov obtained the distribution F for his omega(2)-test in the form of a certain series. F is identical to the distribution of the the Brownian bridge in the L-2 norm. Smirnov, Kac and Shepp determined the Laplace-Stieltjes transform of F. Anderson and Darling expressed F in terms of Bessel functions. In the present paper we compute the moments of F and their asymptotics, obtain expansions of F and its density f in terms of the parabolic cylinder functions and Laguerre functions, and determi...
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作者：Asselah, A; Pra, PD
作者单位：Aix-Marseille Universite; Polytechnic University of Milan
摘要：We study quasi-stationary measures for conservative particle systems in the infinite lattice. Existence of quasi-stationary measures is established for a fairly general class of reversible systems. For the special cases of a system of independent random walks and the symmetric simple exclusion process, it is shown that qualitative features of quasi-stationary measures change drastically with dimension.
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作者：Bertoin, J
作者单位：Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Aldous and Pitman have studied the asymptotic behavior of the additive coalescent processes using a nested family random forests: derived by logging certain inhomogeneous continuum random trees. Here we propose a different approach based on partitions of the unit inter val induced by certain bridges with exchangeable increments. The analysis is made simple by an interpretation in terms of an aggregating server system.
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作者：Fill, JA; Machida, M
作者单位：Johns Hopkins University; Utah System of Higher Education; Utah State University
摘要：We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) f when the measures are indexed by another poset A. We give counterexamples to show that the two notions are not always equivalent, but for various large classes of f we also present conditions on the poset A that are necessary and sufficient for equivalence. When A = f the condition that the cover graph of f have no cycles is neces...
