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作者：ALABERT, A; FERRANTE, M; NUALART, D
作者单位：University of Padua; University of Barcelona
摘要：The purpose of this paper is to prove a characterization of the conditional independence of two independent random Variables given a particular functional of them, in terms of a factorization property. As an application we discuss the Markov field property for solutions of stochastic differential equations with a boundary condition involving the values of the process at times t = 0 and t = 1.
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作者：KHOSHNEVISAN, D
摘要：Let W be a real-valued, two-parameter Brownian sheet. Let us define N(t; h) to be the total number of bubbles of W in [0, t](2), whose maximum height is greater than h. Evidently, lim(h down arrow 0) N(t; h) = infinity and lim(t) (up arrow) (infinity) N(t; h) = infinity. It is the goal of this paper to provide fairly accurate estimates on N(t; h) both as t --> infinity and as h --> 0. Loosely speaking, we show that there are of order h(-3) many such bubbles as h down arrow 0 and t(3) many, as ...
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作者：QUASTEL, J
摘要：The hydrodynamic limit appears as a law of large numbers for rescaled density profiles of a large stochastic system. We study the large deviations from this scaling limit for a particular nongradient system, the nongradient version of the Ginzburg-Landau model.
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作者：TALAGRAND, M
作者单位：University System of Ohio; Ohio State University
摘要：Consider a mean zero random variable X, and an independent sequence (X(n)) distributed like X. We show that the random Fourier series Sigma(n greater than or equal to 1) n(-1)X(n) exp(2i pi nt) converges uniformly almost surely if and only if E(\X\ log log(max(e(e), \X\))) < infinity.
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作者：TOWGHI, N
摘要：In this paper the L(1)-stochastic integral and the mixed stochastic integral of a process Y with respect to a process X is defined in a way that extends Riemann-Stieltjes integration of deterministic functions with respect to X. The L(1)-integral will include the classical Ito integral. However, the concepts of ''filtration'' and adaptability do not play any role; instead, the p-variation of Dolean functions of the processes X and Y is the determining factor.
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作者：KERSTING, G; KLEBANER, FC
作者单位：University of Melbourne
摘要：We give sharp sufficient conditions for nonexplosions and explosions in Markov pure jump processes in terms of the holding time parameters and moments of the jump distributions.
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作者：LIAO, M; ZHENG, WA
作者单位：University of California System; University of California Irvine
摘要：Let rho(t) be the radial part of a Brownian motion in an n-dimensional Riemannian manifold M starting at x and let T = T-epsilon be the first time t when rho(t) = epsilon. We show that E[rho(t boolean AND T)(2)] = nt - (1/6)S(x)t(2) + o(t(2)), as t down arrow 0, where S(x) is the scalar curvature. The same formula holds for E[rho(t)(2)] under some boundedness condition on M.
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作者：Bell, DR; Mohammed, SEA
作者单位：Southern Illinois University System; Southern Illinois University
摘要：We establish the existence of smooth densities for solutions of Rd-valued stochastic hereditary differential systems of the form dx(t) = H(t, x) dt + g(t, x(t - r)) dW(t). In the above equation, W is an n-dimensional Wiener process, r is a positive time delay, H is a nonanticipating functional defined on the space of paths in R(d) and g is an n X d matrix-valued function defined on [0, infinity) X R(d), such that gg* has degeneracies of polynomial order on a hypersurface in R(d). In the course...
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作者：Griffin, PS; McConnell, TR
摘要：Let T-r be the first time a sum S-n of nondegenerate i.i.d. random variables leaves a ball of radius r in some given norm on R(d). In the case of the Euclidean norm we completely characterize LP-boundedness of the overshoot parallel to S(Tr)parallel to - r in terms of the underlying distribution. For more general norms we provide a similar characterization under a smoothness condition on the norm which is shown to be very nearly sharp. One of the key steps in doing this is a characterization o...
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作者：LYONS, R; PEMANTLE, R; PERES, Y
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
摘要：The Kesten-Stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process, shelving that an L log L condition is decisive. In critical and subcritical cases, results of Kolmogorov and later authors give the rate of decay of the probability that the process survives at least n generations. We give conceptual proofs of these theorems based on comparisons of Galton-Watson measure to another measure on the space of trees. This approach also explains Yaglom's ...
