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作者：Ho, HC; Hsing, T
作者单位：Academia Sinica - Taiwan; Texas A&M University System; Texas A&M University College Station
摘要：Let X-n = Sigma(i=1)(infinity) alpha(i) epsilon(n-i), where the epsilon(i) are i.i.d. with mean 0 and finite second moment and the ai are either summable or regularly varying with index epsilon (- 1, - 1/2). The sequence {X-n} has short memory in the former case and long memory in the latter. For a large class of functions K, a new approach is proposed to develop both central (root n rate) and noncentral (non-root n rate) limit theorems for S-N = Sigma(n=1)(N) [K(X-n) - EK(X-n)]. Specifically,...
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作者：Kesten, H
作者单位：Cornell University
摘要：Let {X-i}(i greater than or equal to 1) be i.i.d. random variables with common distribution function F-1 and let S-n = Sigma(1)(n) X-i. We find a necessary and sufficient condition (directly in terms of Fl for the existence of sequences of constants (a,) and {beta(n)} with beta(n) up arrow infinity such that 0 < lim inf beta(n)(-1) max(j less than or equal to n) /S-j-alpha(j)/ < infinity w.p.1., and such that for any choice of <(alpha)over tilde>(n), it hold w.p.1 that lim inf beta(n)(-1) max(...
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作者：Wang, FY
作者单位：Beijing Normal University; University of Warwick
摘要：By using logarithmic transformations, an explicit lower bound estimate of heat kernels is obtained for diffusion processes on Riemannian manifolds. This estimate is sharp for both short and long times, especially for heat kernels on a compact manifold, and is extended to manifolds with unbounded curvature.
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作者：Fannjiang, A; Komorowski, T
作者单位：University of California System; University of California Davis; Michigan State University
摘要：We study the asymptotic behavior of Brownian motion in steady, unbounded incompressible random flows. We prove an invariance principle for almost all realizations of random flows. The key compactness result is obtained by Moser's iterative scheme in PDE theory.
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作者：Zhang, LX
作者单位：Zhejiang University
摘要：Let (X-n; n greater than or equal to 0) be a sequence of random variables. We consider its geometrically weighted series xi(beta) = Sigma(n=0)(infinity) beta(n) X-n for 0 < beta < 1. This paper proves that xi(beta) can be approximated by Sigma(n=0)(infinity) beta(n) Y-n under some suitable conditions, where (Y-n; n greater than or equal to 0) is a sequence of independent normal random variables. Applications to the law of the iterated logarithm for xi(beta) are also discussed.
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作者：Krylov, NV
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Several stochastic partial differential equations are derived for multidimensional superdiffusions.
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作者：Klenke, A
作者单位：University of Erlangen Nuremberg
摘要：In this paper we will investigate the long time behavior of critical branching Brownian motion and (finite variance) super-Brownian motion (the so-called Dawson-Watanabe process) on R-d. These processes are known to be persistent if d greater than or equal to 3; that is, there exist nontrivial equilibrium measures. If d less than or equal to 2, they cluster; that is, the processes converge to the 0 configuration while the surviving mass piles up in so-called clusters. We study the spatial prof...
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作者：Rheinlander, T; Schweizer, M
作者单位：Technical University of Berlin
摘要：Let X be an R-d-valued continuous semimartingale, T a fixed time horizon and Theta the space of all R-d-valued predictable X-integrable processes such that the stochastic integral G(theta) = integral theta dX is a square-integrable semimartingale. A recent paper gives necessary and sufficient conditions on X for G(T)(Theta) to be closed in L-2(P). In this paper, we describe the structure of the L-2-projection mapping an F-T-measurable random variable H is an element of L-2(P) on GT(Theta) and ...
