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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：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：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...
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作者：GOGGIN, EM
摘要：Suppose the random variables (X(N), Y(N)) on the probability space (OMEGA(N), F(N), P(N)) converge in distribution to the pair (X, Y) on (OMEGA, F, P), as N --> infinity. This paper seeks conditions which imply convergence in distribution of the conditional expectations E(PN){F(X(N))\Y(N)} to E(P){F(X)\Y}, for all bounded continuous functions F. An absolutely continuous change of probability measure is made from P(N) to a measure Q(N) under which X(N) and Y(N) are independent. The Radon-Nikody...
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作者：BOBKOV, SG
作者单位：Syktyvkar State University
摘要：An isoperimetric property of exponential distributions with respect to the supremum distance in R(n) is proved and applied to stochastic processes linearly generated by i.i.d. positive random values.
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作者：BURKHOLDER, DL
摘要：This paper contains sharp norm, maximal, escape and exponential inequalities for stochastic integrals in which the integrator is either a nonnegative submartingale or a nonnegative supermartingale. Analogous inequalities hold for Ito processes and for smooth functions on Euclidean domains.
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作者：KALPAZIDOU, S
摘要：Let P(h) = (p(ij)(h),i,j= 1,2, ..., n),h greater-than-or-equal-to 0,n greater-than-or-equal-to 1, be a transition matrix function defining an irreducible recurrent continuous parameter Markov process. Let (S(i), i = 1, 2, ..., n) be a partition of the circle into sets S(i) each consisting of a finite union of arcs A(kl). Let f(t) be a rotation of length t of the circle, and denote Lebesgue measure by lambda. We generalize and prove for the transition matrix function P(h) a theorem of Cohen (n ...
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作者：LIGGETT, TM
摘要：The threshold voter models considered in this paper are special cases of the nonlinear voter models which were introduced recently by Cox and Durrett. They are spin systems on Z(d) with transition rates [GRAPHICS] This system is known to cluster if N = d = 1, and to coexist if N greater-than-or-equal-to 4 in one dimension and if N is reasonably large in other dimensions. Cox and Durrett conjectured that it coexists in all cases except N = d = 1. In this paper, we prove this conjecture. The pro...
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作者：MARTON, K; SHIELDS, PC
作者单位：University System of Ohio; University of Toledo; Eotvos Lorand University
摘要：The kth-order joint distribution for an ergodic finite-alphabet process can be estimated from a sample path of length n by sliding a window of length k along the sample path and counting frequencies of k-blocks. In this paper the problem of consistent estimation when k = k(n) grows as a function of n is addressed. It is shown that the variational distance between the true k(n)-block distribution and the empirical k(n)-block distribution goes to 0 almost surely for the class of weak Bernoulli p...
