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作者：FREIDLIN, MI; WENTZELL, AD
作者单位：Lomonosov Moscow State University
摘要：We consider semilinear parabolic PDE's with fast oscillating boundary conditions. The central limit theorem and limit theorems for probabilities of large deviations for the solutions of such problems are proved.
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作者：MELFI, VF
作者单位：University of Michigan System; University of Michigan
摘要：An analogue of the Lai-Siegmund nonlinear renewal theorem is proved for processes of the form S(n) + xi(n), where {S(n)} is a Markov random walk. Specifically, Y0, Y1,... is a Markov chain with complete separable metric state space; X1, X2,... is a sequence of random variables such that the distribution of X(i) given {Y(j), j greater-than-or-equal-to 0} and {X(j), j not-equal i} depends only on Y(i-1) and Y(i); S(n) = X1 + ... +X(n); and {xi(n)} is slowly changing, in a sense to be made precis...
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作者：INGLOT, T; KALLENBERG, WCM; LEDWINA, T
作者单位：University of Twente
摘要：Strong moderate deviation theorems are concerned with relative errors in the tails caused by replacing the exact distribution function by its limiting distribution function. A new approach for deriving such theorems is presented using strong approximation inequalities. In this way a strong moderate deviation theorem is obtained for statistics of the form T(alpha(n)), where T is a sublinear functional and alpha(n) is the empirical process. The basic theorem is also applied on linear combination...
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作者：SHEPP, LA; ZEITOUNI, O
作者单位：Technion Israel Institute of Technology
摘要：It is proven that, for any deterministic L2[0, 1] function phi(t), E(exp integral-1/0-phi(t)dw(t)\parallel-to w parallel-to < epsilon) --> 1 as epsilon --> 0, where w(t) is a standard Brownian motion and parallel-to . parallel to is any reasonable norm on C0[0, 1]. Applications to the computation of Onsager-Machlup functionals are pointed out.
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作者：BRYC, W
摘要：The large deviation principle for the empirical field of a stationary Z(d)-indexed random field is proved under strong mixing dependence assumptions. The strong mixing coefficients considered allow us to separate the ratio-mixing condition used in the literature into a part directly responsible for the (nonuniform) large deviation principle and another one, which is used when the state space is noncompact. Results are applied to obtain variants of recent large deviation theorems for Markov cha...
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作者：HUGHES, HR
摘要：Let X(t) be Brownian motion on a Riemannian manifold M started at m and let T be the first time X(t) exits a normal ball about m. The first exit time T for M = S3 X H-3 has the same distribution as the first exit time for M = R6. For M = S3 X H-3, T and X(T) are independent random variables.
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作者：LI, DL; RAO, MB; WANG, XC
作者单位：Jilin University; North Dakota State University Fargo
摘要：Let X(nBAR) nBAR is-an-element-of N(d), be a field of independent real random variables, where N(d) is the d-dimensional lattice. In this paper, the law of the iterated logarithm is established for such a field of random variables. Theorem 1 brings into focus a connection between a certain strong law of large numbers and the law of the iterated logarithm. A general technique is developed by which one can derive the strong law of large numbers and the law of the iterated logarithm, exploiting t...
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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 vectors leaves the sphere of radius r. The spheres are determined by some given norm on R(d) which need not be the Euclidean norm. As a particular case of our results, we obtain, for mean-zero random vectors and each 0 < p < infinity and 0 less-than-or-equal-to q < infinity, necessary and sufficient conditions on the distribution of the summands to have E(parallel-to S(T(r))parallel-to - r)P = O(r(q)) as r --> infinity. We al...
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作者：CSAKI, E; CSORGO, M
作者单位：Carleton University
摘要：Let {GAMMA(t), t is-an-element-of R} be a Banach space B-valued stochastic process. Let P be the probability measure generated by GAMMA(.). Assume that GAMMA(.) is P-almost surely continuous with respect to the norm parallel-to parallel-to of B and that there exists a positive nondecreasing function sigma(a), a > 0, such that P{parallel-to GAMMA(t + a) - GAMMA(t)parallel-to greater-than-or-equal-to x-sigma(a)} less-than-or-equal-to K exp(-gamma-x(beta) with some K, gamma, beta > 0. Then, assum...
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作者：FISHER, E
摘要：The Kolmogorov law of the iterated logarithm fails when the boundedness condition on the increments is relaxed. In this paper, we consider this in the martingale setting and establish a lower bound, extending a result known in the independent case.
