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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：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：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...
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作者：Arnaudon, M; Thalmaier, A
作者单位：Universite de Poitiers; University of Bonn
摘要：We characterize Yang-Mills connections in vector bundles in terms of covariant derivatives of stochastic parallel transport along variations of Brownian bridges on the base manifold. In particular, we prove that a connection in a vector bundle E is Yang-Mills if and only if the covariant derivative of parallel transport along Brownian bridges (in the direction of their drift) is a local martingale, when transported back to the starting point. We present a Taylor expansion up to order 3 for sto...
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作者：Bass, RF; Chen, ZQ
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：where W-t is d-dimensional Brownian motion with d greater than or equal to 2 and the ith component of At is a process of bounded variation that stands in the same relationship to a measure pi(i) as integral(0)(t) f(X-s) ds does to the measure f (x) dx. We prove weak existence and uniqueness for the above stochastic differential equation when the measures pi(i) are members of the Kato class Kd-1. As a typical example, we obtain a Brownian motion that has upward drift when in certain fractal-lik...
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作者：del Barrio, E; Giné, E; Matrán, C
作者单位：Universidad de Valladolid; University of Connecticut
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作者：Crisan, D
作者单位：Imperial College London
摘要：In Crisan, Gaines and Lyons [SIAM J Appl. Probab. 58 (1998) 313-3421 we describe a branching particle algorithm that produces a particle approximation to the solution of the Zakai equation and find an upper bound for the rate of convergence of the mean square error. In this paper, the exact rate of convergence of the mean square error is deduced. Also, several variations of the branching algorithm with better rates of convergence are introduced.
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作者：Gyöngy, I; Krylov, N
作者单位：University of Edinburgh; University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider two stochastic partial differential equations du(epsilon)(t) = (L(r)u(epsilon)(t) + f(r)(t))dV(epsilont)(r) + (M(k)u(epsilon)(t) + g(k)(t)) odY(t)(k), epsilon = 0, 1, driven by the same multidimensional martingale Y = (Y-k) and by different increasing processes V-0(r), V-1(r), r = 1, 2,..., d(1), where L-r and M-k are second- and first-order partial differential operators and o stands for the Stratonovich differential. We estimate the moments of the supremum in t of the Sobolev nor...
