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作者：IOFFE, D
作者单位：University of California System; University of California Davis
摘要：If L generates a transient diffusion, then the corresponding exterior Dirichlet problem (EP) has in general many bounded solutions. We consider perturbations of L by a first-order term and assume that EP can be solved uniquely for each perturbed operator. Then as the perturbation tends to 0, the sequence of perturbed solutions may converge to a solution of the original EP. Using a skew-product representation of diffusions, we give an integral criterion for the uniqueness of this limit and show...
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作者：SEPANSKI, SJ
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：We consider the problem of when the bootstrap sample mean, appropriately normalized and centered, converges in distribution along almost every sample path. We allow the normalizing sequence to be an arbitrary sequence of positive random variables. It is proved that the only possible normalizing sequence is essentially (SIGMA(i=1)n X(i)2)1/2. Furthermore, if the bootstrap sample mean converges along almost every sample path, then either the variance is finite or else the distribution of X is ex...
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作者：BAI, ZD
摘要：In this paper, we shall develop certain inequalities to bound the difference between distributions in terms of their Stieltjes transforms. Using these inequalities, convergence rates of expected spectral distributions of large dimensional Wigner and sample covariance matrices are established. The paper is organized into two parts. This is the first part, which is devoted to establishing the basic inequalities and a convergence rate for Wigner matrices.
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作者：JAKUBOWSKI, A
摘要：Let (X(k))k is-an-element-of N be a nonstationary sequence of random variables. Sufficient conditions are found for the existence of an independent sequence (X(k)}k is-an-element-of N such that sup(x is-an-element-of R)\P(M(n) less-than-or-equal-to x)\ - P(M(n) less-than-or-equal-to x)\ --> 0 as n --> infinity, where M(n) and M(n) are nth partial maxima for (X(k)) and {X(k)}, respectively.
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作者：SCHROEDER, C
摘要：Let (X, B) be a compact metric space with B the sigma-field of Borel sets. Suppose this is the state space of a discrete parameter Markov process. Let C be a closed convex set of probability measures on X. Known results on the asymptotic behavior of the probability that the empirical distributions P(n) belong to C and new results on the Markov process distribution of omega0,..., omega(n-1) under the condition P(n) is-an-element-of C are obtained simultaneously through a large deviations estima...
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作者：EIZENBERG, A; FREIDLIN, M
作者单位：University System of Maryland; University of Maryland College Park
摘要：We continue the study of the asymptotic behavior of Markov processes (X(epsilon)(t), v(epsilon)(t)) corresponding to systems of elliptic PDE with a small parameter epsilon > 0. In the present paper we consider the case where the process (X(epsilon)(t), v(epsilon)(t)) can leave a given domain D only due to large deviations from the degenerate process (X0(t), v0(t)). In this way we study the limit behavior of solutions of corresponding Dirichlet problems.
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作者：BAI, ZD
摘要：In the first part of the paper, we developed certain inequalities to bound the difference between distributions in terms of their Stieltjes transforms and established a convergence rate of expected spectral distributions of large Wigner matrices. The second part is devoted to establishing convergence rates for the sample covariance matrices, for the cases where the ratio of the dimension to the degrees of freedom is bounded away from 1 or close to 1, respectively.
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作者：ADLER, RJ; ROSEN, JS
作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：The Brownian and stable density processes are distribution valued processes that arise both via limiting operations on infinite collections of Brownian motions and stable Levy processes and as the solutions of certain stochastic partial differential equations. Their (self-) intersection local times (ILT's) of various orders can be defined in a manner somewhat akin to that used to define the self-intersection local times of simple R(d)-valued processes; that is, via a limiting operation involvi...
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作者：HILDEBRAND, M
作者单位：University of Michigan System; University of Michigan; Harvard University
摘要：This paper considers random processes of the form X(n+1) = a(n)X(n) + b(n) (mod p), where X0 = 0 and the sequences a(n) and b(n) are independent with a(n) identically distributed for n = 0, 1, 2.... and b(n) identically distributed for n = 0, 1, 2,... . Chung, Diaconis and Graham studied such processes where a(n) = 2 always; this paper considers more general distributions for a(n) and b(n). The question is how long does it take these processes to get close to the uniform distribution? If an is...
