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作者：Mytnik, L; Perkins, E
作者单位：Technion Israel Institute of Technology; University of British Columbia
摘要：This paper establishes the continuity of the density of (1 + beta)-stable super-Brownian motion (0 < beta < 1) for fixed times in d = 1, and local unboundedness of the density in all higher dimensions where it exists. We also prove local unboundedness of the density in time for a fixed spatial parameter in any dimension where the density exists, and local unboundedness of the occupation density (the local time) in the spatial parameter for dimensions d greater than or equal to 2 where the loca...
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作者：Khoshnevisan, D; Xiao, YM; Zhong, YQ
作者单位：Utah System of Higher Education; University of Utah; Michigan State University; Chinese Academy of Sciences
摘要：The primary goal of this paper is to study the range of the random field X (t) = Sigma(j=1)(N) X-j (t(j)), where X-1,...,X-N are independent Levy processes in R-d. To cite a typical result of this paper, let us suppose that psi(i) denotes the Levy exponent of X-i for each i = 1,...,N. Then, under certain mild conditions, we show that a necessary and sufficient condition for X(RN) to have positive d-dimensional Lebesgue measure is the integrability of the function R-d There Exists xi bar right ...
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作者：Gradinaru, M; Russo, F; Vallois, P
作者单位：Universite de Lorraine; Universite Paris 13
摘要：Given a locally bounded real function g, we examine the existence of a 4-covariation [g(B-H), BH, BH, BH], where BH is a fractional Brownian motion with a Hurst index H greater than or equal to (1)/(4). We provide two essential applications. First, we relate the 4-covariation to one expression involving the derivative of local time, in the case H = (1)/(4), generalizing an identity of Bouleau-Yor type, well known for the classical Brownian motion. A second application is an Ito formula of Stra...
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作者：Revelle, D
作者单位：University of California System; University of California Berkeley
摘要：This article examines the rate of escape for a random walk on G Z and proves laws of the iterated logarithm for both the inner and outer radius of escape. The class of G for which these results hold includes finite, G as well as groups of the form H Z, so the construction can be iterated. Laws of the iterated logarithm are also found for random walk on Baumslag-Solitar groups and a discrete version of the Sol geometry.
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作者：Li, WBV
作者单位：University of Delaware
摘要：Consider the first exit time tau(D) of a (d + 1)-dimensional Brownian motion from an unbounded open domain D = {(x, y) is an element of Rd+1 : y > f(x), x is an element of R-d} starting at (x(0), f(x(0)) + 1) is an element of Rd+1 for some x(0) is an element of R-d, where the function f(x) on R-d is convex and f(x) --> infinity as the Euclidean norm \x\ --> infinity. Very general estimates for the asymptotics of logP(tau(D) > t) are given by using Gaussian techniques. In particular, for f(x) e...
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作者：Burdzy, K; Kulczycki, T
作者单位：University of Washington; University of Washington Seattle; Polish Academy of Sciences; Wroclaw University of Science & Technology
摘要：Let X(t) be the symmetric alpha-stable process in R-d, alpha is an element of (0, 2), d greater than or equal to 2. For f:(0, 1) --> (0, infinity) let D (f) be the thorn {x is an element of R-d : x(1) is an element of (0, 1), \(x(2), - - -, x(d))\ < f (x(1))}. We give an integral criterion in terms of f for the existence of a random time s such that X(t) remains in X(s) + (D) over bar (f) for all t is an element of [s, s + 1).
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作者：Talagrand, M
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University System of Ohio; Ohio State University
摘要：Given a bounded class of functions, we introduce a combinatorial quantity (related to the idea of Vapnik-Chervonenkis classes) that is much more explicit than the Koltchinskii-Pollard entropy, but is proved to be essentially of the same order.
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作者：Csörgo, M; Szyszkowicz, B; Wang, QY
作者单位：Carleton University; Australian National University
摘要：Let X, X-1, X-2,... be i.i.d. nondegenerate random variables, S-n = Sigma(j=1)(n) X-j and V-n(2) = Sigma(j=1)(n) X-j(2). We investigate the asymptotic behavior in distribution of the maximum of self-normalized sums, max(1less than or equal tokless than or equal ton) S-k/V-k, and the law of the iterated logarithm for self-normalized sums, S-n/V-n, when X belongs to the domain of attraction of the normal law. In this context, we establish a Darling-Erdos-type theorem as well as an Erdos-Feller-K...
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作者：Junge, M; Xu, QH
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Universite Marie et Louis Pasteur
摘要：We investigate martingale inequalities in noncommutative L-p-spaces associated with a von Neumann algebra equipped with a faithful normal state. We prove the noncommutative analogue of the classical Burkholder inequality on the conditioned (or little) square function and extend the noncommutative Burkholder-Gundy inequalities from Comm. Math. Phys. 189 (1997) 667-698 to this nontracial setting. We include several related results.
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作者：Marcus, MB; Rosen, J
作者单位：City University of New York (CUNY) System; City College of New York (CUNY); City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：A new global isomorphism theorem is obtained that expresses the local times of transient regular diffusions under P-x,P-y, in terms of related Gaussian processes. This theorem immediately gives an explicit description of the local times of diffusions in terms of 0th order squared Bessel processes similar to that of Eisenbaum and Ray's classical description in terms of certain randomized fourth order squared Bessel processes. The proofs given are very simple. They depend on a new version of Kac...
