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作者：TALAGRAND, M
作者单位：University System of Ohio; Ohio State University
摘要：Consider 0 < alpha < 1 and the Gaussian process Y(t) on R(N) with covariance E(Y(t)Y(s)) = \t\(2 alpha) + \s\(2 alpha) - \t - s\(2 alpha), where \t\ is the Euclidean norm of t. Consider independent copies X(1),...,X(d) Of Y and the process X(t) = (X(1)(t),...,X(d)(t)) valued in R(d). In the transient case (N < alpha d) we show that a.s. for each compact set L of R(N) with nonempty interior, we have 0 < mu(phi)(X(L)) < infinity, where mu(phi), denotes the Hausdorff measure associated with the f...
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作者：Baldi, P
摘要：We study the asymptotics of the exit probability P-x, s(epsilon){tau less than or equal to T), where tau is the exit time from an open set and P-x, s(epsilon), is the law of a diffusion process with a small parameter epsilon multiplying the diffusion coefficient. We consider the case of the Brownian bridge in many dimensions, this choice being motivated by applications to numerical simulation. The method uses recent results reducing the problem to the solution of a system of linear first-order...
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作者：COLLET, P; MARTINEZ, S; SANMARTIN, J
作者单位：Universidad de Chile
摘要：If (X(t)) is a one-dimensional diffusion corresponding to the operator L = 1/2 partial derivative(xx) - alpha partial derivative(x) starting from x > 0 and T-a is the hitting time of a, we prove that under suitable conditions on the drift coefficient the following Limit exists: For All s > 0, For All Alpha is an element of f(s), lim(t-->infinity)P(x)(X is an element of Alpha\T-0 > t). We characterize this limit as the distribution of an h-like process, h satisfying Lh = - eta h, h(0) = 0, h'(0...
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作者：NEWMAN, CM; PIZA, MST
作者单位：University of California System; University of California Irvine
摘要：We consider stochastic growth models, such as standard first-passage percolation on Z(d), where to leading order there is a linearly growing deterministic shape. Under natural hypotheses, we prove that for d = 2, the shape fluctuations grow at least logarithmically in all directions. Although this bound is far from the expected power law behavior with exponent chi = 1/3, it does prove divergence. With additional hypotheses, we obtain inequalities involving chi and the related exponent xi (whic...
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作者：WANG, JG
摘要：Let M be a locally square integrable martingale with predictable quadratic Variance (M) and let Delta M = M - M_ be the jump process of M. In this paper, under the Various restrictions on Delta M, the different increasing rates of M in terms of (M) are obtained. For stochastic integrals X = B . M of the predictable process B with respect to M, the a.s. asymptotic behavior of X is also discussed under restrictions on the rates of increase of B and the restrictions on the conditional distributio...
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作者：CUZICK, J; GINE, E; ZINN, J
作者单位：University of Connecticut; University of Connecticut; Texas A&M University System; Texas A&M University College Station; Texas A&M University System; Texas A&M University College Station
摘要：Let X, X(i) be i.i.d. real random variables with EX(2) = infinity. Necessary and sufficient conditions in terms of the law of X are given for (1/gamma(n)) max(1 less than or equal to i 0 a.s. in general and for (1/gamma(n)) Sigma(1 less than or equal to i not equal j less than or equal to n) X(i)X(j) --> 0 a.s. when the variables X(i) are symmetric or regular and the normalizing sequence {gamma(n)} is (mildly) regular. The rates of a.s. convergence of sums and maxima of products turn out to be...
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作者：Cairoli, R; Dalang, RC
作者单位：Tufts University
摘要：This paper is motivated by remarkable results of Mandelbaum, Shepp and Vanderbei concerning an optimal switching problem for two Brownian motions. In this paper, the discrete form of this problem, in which the Brownian motions are replaced by random walks, is studied and solved without any restriction on the boundary data. The method proposed here involves uncovering the structure of the solution using combinatorial and geometric arguments, and then providing a characterization for the two typ...
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作者：Stong, R
摘要：In this paper we give sharp bounds on the eigenvalues of the natural random walk on the Burnside group B(3, n). Most of the argument uses established geometric techniques for eigenvalue bounds. However, the most interesting bound, the upper bound on the second largest eigenvalue, cannot be done by existing techniques. To give a bound we use a novel method for bounding the eigenvalues of a random walk on a group G (or equivalently its Cayley graph). This method works by choosing eigenvectors wh...
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作者：RIO, E
摘要：Let (X(i))(i is an element of Z) be a strictly stationary and strongly mixing sequence of real-valued mean zero random variables. Let (alpha(n))(n>0) be the sequence of strong mixing coefficients. We define the strong mixing fraction alpha (.) by alpha(t) = alpha([t]) and we denote by Q the quantile function of \X(0)\. Assume that (*) integral(0)(1) alpha(-1)(t)Q(2)(t)dt < infinity, where f(-1) denotes the inverse of the monotonic function f. The main result of this paper is that the functiona...
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作者：HSING, TL
摘要：It is shown that Sigma(i=1)(n) X(n) and max(i=1)(n)X(i) are asymptotically independent if {X(i)} is strongly mixing and Sigma(i=1)(n)X(i) is asymptotically Gaussian. This generalizes a result of Anderson and Turkman.
