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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：RIO, E
摘要：Let (X(i))i is-an-element-of Z(+)d be an array of zero-mean independent identically distributed random vectors with values in R(k) with finite variance, and let J be a class of Borel subsets of [0, 1]d. If, for the usual metric, J is totally bounded and has a convergent entropy integral, we obtain a strong invariance principle for an appropriately smoothed version of the partial-sum process {SIGMA(i is-an-element-of nu S)X(i): S is-an-element-of J} with an error term depending only on J and on...
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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：JACKA, SD
摘要：Let X be a semimartingale, and S its Snell envelope. Under the assumption that X and S are continuous semimartingales in H-1, this article obtains a new, maximal, characterisation of S, and gives an application to the optimal stopping of functions of diffusions. We present a counterexample to the standard assertion that S is just ''a martingale on the go-region and X on the stop-region.''
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作者：FREIDLIN, MI; WENTZELL, AD
摘要：A number of asymptotic problems for ''classical'' stochastic processes leads to diffusion processes on graphs. In this paper we study several such examples and develop a general technique for these problems. Diffusion in narrow tubes, processes with fast transmutations and small random perturbations of Hamiltonian systems are studied.
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作者：EISENBAUM, N; KASPI, H
作者单位：Technion Israel Institute of Technology
摘要：Let X be a Markov process on an interval E of R, with lifetime zeta, admitting a local time at each point and such that P(x)(X hits y) > 0 for all x, y in E. We prove here that the local times process (L(zeta)x, x is-an-element-of E) is a Markov process if and only if X has fixed birth and death points and X has continuous paths. The sufficiency of this condition has been established by Ray, Knight and Walsh. The necessity is proved using arguments based on excursion theory. This result has be...
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作者：FALK, M; MAROHN, F
摘要：It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function F from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if F is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an iid sample, whether in terms of the distribution of the largest order ...
