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作者：Kupsa, M; Lacroix, Y
作者单位：Charles University Prague; Universite de Toulon
摘要：In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class [GRAPHICS] Note that all possible asymptotics are absolutely continuous.
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作者：Tindel, S
作者单位：Universite de Lorraine
摘要：In this note we show how to generalize the stochastic calculus method introduced by Comets and Neveu [Comm. Math. Phys. 166 (1995) 549-564] for two models of spin glasses, namely, the SK model with external field and the perceptron model. This method allows to derive quite easily some fluctuation results for the free energy in those two cases.
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作者：Ruzmaikina, A; Aizenman, M
作者单位：University of Virginia; Purdue University System; Purdue University; Purdue University System; Purdue University; Princeton University; Princeton University
摘要：We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. Quasi-stationary states are defined as probability measures, on the sigma-algebra generated by the gap variables, for which joint distribution of gaps between particles is invariant under the time evolution. Examples are provided by Poisson processes with densities of the form rho(dx) = e(-sx) sdx, with s > 0, and linear superpositions of such measures. We show that, convers...
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作者：Einmahl, U; Deli, L
作者单位：Vrije Universiteit Brussel; Lakehead University
摘要：Let {X, X-n; n > 1} be a sequence of i.i.d. mean-zero random variables, and let S-n = Sigma(n)(i) (=1) X-i, n >= 1. We establish necessary and sufficient conditions for having with probability 1, 0 < lim sup(n ->infinity)vertical bar Sn vertical bar/root nh(n) < infinity where h is from a suitable subclass of the positive, nondecreasing slowly varying functions. Specializing our result to h(n) = (log log n)(P), where p > 1 and to h(n) = (log n)(r), r > 0, we obtain analogues of the Hartman-Win...
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作者：Ferrari, PL; Spohn, H
作者单位：Technical University of Munich
摘要：Motivated by the polynuclear growth model, we consider a Brownian bridge b(t) with b(+/- T) = Oconditioned to stay above the semicircle C-T(t) = root T-2 - t(2). In the limit of large T, the fluctuation scale of b(t) - CT(t) is T-1/3 and its time-correlation scale is T-2/3. We prove that, in the sense of weak convergence of path measures, the conditioned Brownian bridge, when properly resealed, converges to a stationary diffusion process with a drift explicitly given in terms of Airy functions...
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作者：Dereich, S; Lifshits, MA
作者单位：Technical University of Berlin; Saint Petersburg State University
摘要：We investigate the Gaussian small ball probabilities with random centers, find their deterministic a.s.-equivalents and establish a relation to infinite-dimensional high-resolution quantization.
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作者：Chen, ZJ; Chen, T; Davison, M
作者单位：Shandong University; Western University (University of Western Ontario)
摘要：In this paper we consider two ways to generalize the mathematical expectation of a random variable, the Choquet expectation and Peng's g-expectation. An open question has been, after making suitable restrictions PP to the class of random variables acted on by the Choquet expectation, for what class of expectation do these two definitions coincide? In this paper we provide a necessary and sufficient condition which proves that the only expectation which lies in both classes is the traditional l...
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作者：Piau, D
作者单位：Universite Claude Bernard Lyon 1
摘要：We extend in two directions our previous results about the sampling and the empirical measures of immortal branching Markov processes. Direct applications to molecular biology are rigorous estimates of the mutation rates of polymerase chain reactions from uniform samples of the population after the reaction. First, we consider nonhomogeneous processes, which are more adapted to real reactions. Second, recalling that the first moment estimator is analytically known only in the infinite populati...
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作者：Andjel, ED; Guiol, H
作者单位：Aix-Marseille Universite; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble
摘要：We show that if mu is an invariant measure for the long range exclusion process putting no mass on the full configuration, L is the formal generator of that process and f is a cylinder function, then Lf is an element of L-1 (d mu) and integral Lf d mu = 0. This result is then applied to determine (i) the set of invariant and translation-invariant measures of the long range exclusion process on Z(d) when the underlying random walk is irreducible; (ii) the set of invariant measures of the long r...
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作者：Samorodnitsky, G
作者单位：Cornell University
摘要：This paper elucidates the connection between stationary symmetric alpha-stable processes with 0 < alpha < 2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes.
