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作者：FERRARI, PA; GALVES, A; LANDIM, C
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Rouen Normandie
摘要：The first time that the N sites to the right of the origin become empty in a one-dimensional zero-range process is shown to converge exponentially fast, as N --> infinity, to the exponential distribution, when divided by its mean. The initial distribution of the process is assumed to be one of the extremal invariant measures nu(rho), rho is-an-element-of(0, 1), with density rho/(1 - rho). The proof is based on the classical Burke theorem.
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作者：BARLOW, MT; PERKINS, EA
摘要：We show that the historical Brownian motion may be recovered from ordinary super-Brownian motion when the dimension d of the underlying Brownian motion is greater than 4. We outline a proof showing that this conclusion is false if d less than or equal to 3. The state of affairs in the critical dimension d = 4 is left unresolved. Some extensions are given for 1+beta stable branching mechanisms where beta epsilon (0, 1).
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作者：KESTEN, H; MALLER, RA
作者单位：University of Western Australia
摘要：We consider infinite limit points (in probability) for sums and lightly trimmed sums of i.i.d, random variables normalized by a nonstochastic sequence. More specifically, let X(1),X(2),... be independent random variables with common distribution F. Let M(n)((r))) be the rth largest among X(1),...,X,,; also let; X(n)((r)) be the observation with the rth largest absolute value among X(1),...,X(n). Set S-n = Sigma(1)(n)X(i), ((r))S-n = S-n - M(n)((1)) - ... - M(n)((r)) and ((r))(S) over tilde(n) ...
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作者：KHOSHNEVISAN, D
作者单位：University of Washington; University of Washington Seattle
摘要：In this article we are mainly concerned with proving lower bounds on some uniform approximation schemes for the local times of one-dimensional Brownian motion. Consequently, this leads to many exact limit theorems for Brownian local times. The latter results are Paul Levy's occupation time approximation, the downcrossing theorem and an intrinsic construction.
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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...
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作者：DURRETT, R; NEUHAUSER, C
作者单位：University of Southern California
摘要：In this paper we will consider translation invariant finite range particle systems with state space {0,1,..., kappa-1)S with S = epsilonZ(d). De Masi, Ferrari and Lebowitz have shown that if we introduce stirring at rate epsilon-2, then the system converges to the solution of an associated reaction diffusion equation. We exploit this connection to prove results about the existence of phase transitions when the stirring rate is large that apply to a wide variety of examples with state space {0,...
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作者：IMKELLER, P; NUALART, D
作者单位：University of Barcelona
摘要：We present a general criterion for the existence of an occupation density, which is based on the integration by parts formula on Wiener space. This criterion is applied to two particular examples of anticipating processes. First we discuss the case of Brownian motion plus a nonadapted . absolutely continuous drift, and second we consider the case of a Skorohod integral process. Finally a version of Tanaka's formula is proved for the Skorohod integral process.
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作者：YU, B
摘要：Classical empirical process theory for Vapnik-Cervonenkis classes deals mainly with sequences of independent variables. This paper extends the theory to stationary sequences of dependent variables. It establishes rates of convergence for beta-mixing and phi-mixing empirical processes indexed by classes of functions. The method of proof depends on a coupling of the dependent sequence with sequences of independent blocks, to which the classical theory can be applied. A uniform O(n(-s/(1+s))) rat...
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作者：OKAZAKI, Y; SATO, H
作者单位：Kyushu University
摘要：Let X = {X(k)} be an i.i.d. real random sequence, let epsilon = {epsilon(k)} be a Rademacher sequence independent of X and let a = {a(k)} be a deterministic real sequence. The aim of this paper is to prove that the mutual absolute continuity of probability measures induced by {X(k)} and {X(k) + a(k)epsilon(k)} implies a is-an-element-of l4. This is a generalization of a result of Shepp.
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作者：XIA, C
摘要：Let {X,X(n); n greater-than-or-equal-to 1} be a sequence of i.i.d. random variables with values in a separable Banach spacc B and set, for each n, S(n) = X1 + ... + X(n). We give necessary and sufficient conditions in order that [GRAPHICS] where p greater-than-or-equal-to 1. Furthermore, the exact values of the above lim sup are obtained. Some results are the extensions of Strassen's work to the vector settings and some are new even on the real line, The proofs depend on the construction of %a...
