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作者：ALDOUS, D
摘要：Recursive self-similarity for a random object is the property of being decomposable into independent rescaled copies of the original object. Certain random combinatorial objects-trees and triangulations-possess approximate versions of recursive self-similarity, and then their continuous limits possess exact recursive self-similarity. In particular, since the limit continuum random tree can be identified with Brownian excursion, we get a nonobvious recursive self-similarity property for Brownia...
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作者：LYONS, TJ; ZHANG, TS
摘要：We extend the forward-backward martingale approach to Stratonovich integrals developed by Zheng and Lyons to the general context of Dirichlet spaces. From this perspective, it is clear that the Stratonovich integral of an L2 1-form against a Dirichlet process is well defined, coordinate invariant, and obeys appropriate chain rules. The paper continues by examining the tightness and continuity of the mapping from Dirichlet forms to probability measures on path space. Some positive results are o...
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作者：DEHEUVELS, P; MASON, DM
作者单位：University of Delaware
摘要：We introduce the notion of a multivariate local (and tail) empirical process indexed by sets and establish a number of functional laws of the iterated logarithm for such processes. This leads to a unified methodology to study the almost sure behavior of various statistics which are local functionals of the empirical distribution. Such statistics include density estimators and the Bahadur-Kiefer representation.
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作者：GNEDIN, AV
摘要：For any n > 2 we construct an exchangeable sequence of positive continuous random variables, X(1),...,X(n), for which, among all stopping rules, tau, based on the X's, sup(tau) P(X(tau) = X(1) V...V X(n)) is achieved by a rule based only on the relative ranks of the X's.
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作者：VUOLLEAPIALA, J
摘要：Let X(t) be an alpha-self-similar Markov process on (0, infinity) killed when hitting 0. Alpha-self-similar extensions of X(t) to [0, infinity) are studied via Ito execusion theory (entrance laws). We give a condition that guarantees the existence of an extension, which either leaves 0 continuously (a.s.) or (a.s.) jumps from 0 to (0, infinity) according to the ''jumping in'' measure eta(dx) = dx/x(beta+1). Two applications are given: the diffusion case and the ''reflecting barrier process'' o...
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作者：KLEIN, A
摘要：We consider the (inhomogeneous) percolation process on Z(d) x R defined as follows: Along each vertical line {x} x R we put cuts at times given by a Poisson point process with intensity delta(x), and between each pair of adjacent vertical lines {x} x R and {y} x R we place bridges at times given by a Poisson point process with intensity lambda(x, y). We say that (x, t) and (y, s) are connected (or in the same cluster) if there is a path from (x, t) to (y, s) made out of uncut segments of verti...
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作者：DABROWSKI, AR; JAKUBOWSKI, A
作者单位：Nicolaus Copernicus University
摘要：We consider a stationary sequence of associated real random variables and state conditions which guarantee that partial sums of this sequence, when properly normalized, converge in distribution to a stable, non-Gaussian limit. Limit theorems for jointly stable and associated random variables are investigated in detail. In the general case we assume that finite-dimensional distributions belong to the domain of attraction of multidimensional strictly stable laws and that there is a bound on the ...
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作者：GREVEN, A; DENHOLLANDER, F
作者单位：Radboud University Nijmegen
摘要：Let omega = (p(x))(x epsilon Z) be an i.i.d, collection of (0, 1) valued random variables. Given omega, let (X(n))(n greater than or equal to 0) be the Markov chain on Z defined by X(0) = 0 and X(n+1) = X(n)+1(resp.X(n)-1) with probability p(Xn) (resp. 1-p(Xn)). It is shown that X(n)/n satisfies a large deviation principle with a continuous rate function, that is, [GRAPHICS] First, we derive a representation of the rate function I in terms of a variational problem. Second, we solve the latter ...
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作者：DELAPENA, VH; KLASS, MJ
作者单位：Columbia University
摘要：Let X1, X2, ..., X(n) be independent mean-zero random variables and let a(ij), 1 less-than-or-equal-to i,j less-than-or-equal-or n, be an array of constants with a(ii) = 0. We present a method of obtaining the order of magnitude of EPHI(SIGMA1 less-than-or-equal-to i,j less-than-or-equal-to n a(ij)X(i)X(j)) for any such {X(i)} and {a(ij)} and any nonnegative symmetric (convex) function PHI with PHI(0) = 0 such that, for some integer k greater-than-or-equal-to 0, PHI(x2 - k) is convex and simul...
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作者：FERRARI, PA; FONTES, LRG
摘要：We compute the diffusion coefficient of the current of particles through a fixed point in the one-dimensional nearest neighbor asymmetric simple exclusion process in equilibrium. We find D = \p - q\rho(1 - rho)\1 - 2rho\, where p is the rate at which the particles jump to the right, q is the jump rate to the left and rho is the density of particles. Notice that D vanishes if p = q or rho = 1/2. Laws of large numbers and central limit theorems are also proven. Analogous results are obtained for...
