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作者：Van den Berg, Jacob; Kiss, Demeter
作者单位：Centrum Wiskunde & Informatica (CWI); Vrije Universiteit Amsterdam
摘要：Let E be the set of edges of the d-dimensional cubic lattice Z(d), with d >= 2, and let (e), e is an element of E, be nonnegative values. The passage time from a vertex nu to a vertex omega is defined as inf(pi : nu ->omega) Sigma(e is an element of pi) t(e), where the infimum is over all paths pi from nu to omega, and the sum is over all edges e of pi. Benjamini, Kalai and Schramm [2] proved that if the t (e)'s are i.i.d. two-valued positive random variables, the variance of the passage time ...
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作者：van Neerven, Jan; Veraar, Mark; Weis, Lutz
作者单位：Delft University of Technology; Helmholtz Association; Karlsruhe Institute of Technology
摘要：In this article we prove a maximal L-p-regularity result for stochastic convolutions, which extends Krylov's basic mixed L-p(L-q)-inequality for the Laplace operator on R-d to large classes of elliptic operators, both on R-d and on bounded domains in R-d with various boundary conditions. Our method of proof is based on McIntosh's H-infinity-functional calculus, R-boundedness techniques and sharp L-p (L-q)-square function estimates for stochastic integrals in L-q-spaces. Under an additional inv...
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作者：Bendikov, Alexander; Saloff-Coste, Laurent
作者单位：University of Wroclaw; Cornell University
摘要：We study the decay of convolution powers of probability measures without second moment but satisfying some weaker finite moment condition. For any locally compact unimodular group G and any positive function rho : G --> [0, +infinity], we introduce a function Phi(G,rho) which describes the fastest possible decay of n bar right arrow phi((2n)) (e) when phi is a symmetric continuous probability density such that integral rho phi is finite. We estimate Phi(G,rho) for a variety of groups G and fun...
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作者：Kuwae, Kazuhiro
作者单位：Kumamoto University
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作者：Kuwada, Kazumasa
作者单位：Ochanomizu University
摘要：We study an approximation by time-discretized geodesic random walks of a diffusion process associated with a family of time-dependent metrics on manifolds. The condition we assume on the metrics is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow, and no further a priori curvature bound is required. As an application, we construct a coupling by reflection which yields a nice estimate of coupling time, and hence a...
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作者：Patie, P.
作者单位：Universite Libre de Bruxelles
摘要：Let X be a spectrally negative self-similar Markov process with 0 as an absorbing state. In this paper, we show that the distribution of the absorption time is absolutely continuous with an infinitely continuously differentiable density. We provide a power series and a contour integral representation of this density. Then, by means of probabilistic arguments, we deduce some interesting analytical properties satisfied by these functions, which include, for instance, several types of hypergeomet...
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作者：Basrak, Bojan; Krizmanic, Danijel; Segers, Johan
作者单位：University of Zagreb; University of Rijeka; Universite Catholique Louvain
摘要：Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version of this is known to be true as well, the limit process being a stable Levy process. The main result in the paper is that for a stationary, regularly varying sequence for which clusters of high-threshold excesses can be broken down into asymptotically indepe...
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作者：Cohen, Samuel N.; Elliott, Robert J.
作者单位：University of Oxford; University of Adelaide; University of Calgary
摘要：We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic variations of martingales or of the measure integrating the driver. We present conditions for existence and uniqueness of square-integrable solutions, using Lipschitz continuity of the driver. These conditions unite the requirements for existence in continuous and ...
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作者：Ben Arous, Gerard; Fribergh, Alexander; Gantert, Nina; Hammond, Alan
作者单位：New York University; University of Munster; University of Oxford
摘要：We consider a biased random walk X-n on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that there exists an explicit constant gamma = gamma(beta) is an element of (0, 1), depending on the bias beta, such that vertical bar X-n vertical bar is of order n(gamma). Denoting Delta(n) the hitting time of level n, we prove that Delta(n)/n(1/gamma) is tight. Moreover, we show that Delta(n)/n(1/gamma) does not converge in law (at least for large values of beta). We prove that alo...
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作者：Bhamidi, Shankar; van der Hofstad, Remco; van Leeuwaarden, Johan S. H.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology
摘要：We find scaling limits for the sizes of the largest components at criticality for rank-1 inhomogeneous random graphs with power-law degrees with power-law exponent tau. We investigate the case where tau is an element of (3,4), so that the degrees have finite variance but infinite third moment. The sizes of the largest clusters, resealed by n(-(tau-2)/(tau-1)), converge to hitting times of a thinned Levy process, a special case of the general multiplicative coalescents studied by Aldous [Ann. P...
