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作者：Xiong, J
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We study a nonlinear stochastic partial differential equation whose solution is the conditional log-Laplace functional of a superprocess in a random environment. We establish its existence and uniqueness by smoothing out the nonlinear term and making use of the particle system representation developed by Kurtz and Xiong [Stochastic Process. Appl. 83 (1999) 103-126]. We also derive the Wong-Zakai type approximation for this equation. As an application, we give a direct proof of the moment formu...
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作者：Doney, RA
作者单位：University of Manchester
摘要：Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Levy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Levy process versions of many known results about the large-time behavior of random walks. This is illustrated by establishing a comprehensive theorem about Levy processes which converge to infinity in probabi...
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作者：Samorodnitsky, G
作者单位：Cornell University
摘要：We study the partial maxima of stationary alpha-stable processes. We relate their asymptotic behavior to the ergodic theoretical properties of the flow. We observe a sharp change in the asymptotic behavior of the sequence of partial maxima as flow changes from being dissipative to being conservative, and argue that this may indicate a change from a short memory process to a long memory process.
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作者：Becker-Kern, P; Meerschaert, MM; Scheffler, HP
作者单位：Dortmund University of Technology; Nevada System of Higher Education (NSHE); University of Nevada Reno
摘要：Scaling limits of continuous time random walks are used in physics to model anomalous diffusion, in which a cloud of particles spreads at a different rate than the classical Brownian motion. Governing equations for these limit processes generalize the classical diffusion equation. In this article, we characterize scaling limits in the case where the particle jump sizes and the waiting time between jumps are dependent. This leads to an efficient method of computing the limit, and a surprising c...
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作者：Limic, V; Pemantle, R
作者单位：University of British Columbia; University of Pennsylvania
摘要：The purpose of this note is to provide proofs for some facts about the NK model of evolution proposed by Kauffman and Levin. In the case of normally distributed fitness summands, some of these facts have been previously conjectured and heuristics given. In particular, we provide rigorous asymptotic estimates for the number of local fitness maxima in the case when K is unbounded. We also examine the role of the individual fitness distribution and find the model to be quite robust with respect t...
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作者：Marton, K
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences
摘要：Let q(n) be a continuous density function in n-dimensional Euclidean space. We think of q(n) as the density function of some random sequence X-n with values in R-n. For I subset of [1. n], let X-I denote the collection of coordinates X-i, i is an element of I, and let X-I, denote the collection of coordinates X-i, i is not an element of I. We denote by Q(I)(x(I)\x(I)) the joint conditional density function of X-I, given X-I. We prove measure concentration for q in the case when, for an appropr...
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作者：Albeverio, S; Ferrario, B
作者单位：University of Bonn; University of Pavia
摘要：A stochastic Navier-Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure mu(v) whose covariance is given in terms of the enstrophy. Pathwise uniqueness for mu(v)-a.e. initial velocity is proven for solutions having mu(v) as invariant measure.
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作者：Richards, DS
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：Let (L,less than or equal to) be a finite distributive lattice, and suppose that the functions f(1), f(2): L --> R are monotone increasing with respect to the partial order less than or equal to. Given mu a probability measure on L, denote by E(f(i)) the average of f(i) over L with respect to mu, i = 1, 2. Then the FKG inequality provides a condition on the measure g under which the covariance, Cov(f(1), f(2)) := E(f(1)f(2)) - E(f(1))E(f(2)), is nonnegative. In this paper we derive a third-ord...
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作者：Pipiras, V; Taqqu, MS
作者单位：Boston University
摘要：We study stationary stable processes related to periodic and cyclic flows in the sense of Rosinski [Ann. Probab. 23 (1995) 1163-1187]. These processes are not ergodic. We provide their canonical representations, consider examples and show how to identify them among general stationary stable processes. We conclude with the unique decomposition in distribution of stationary stable processes into the sum of four major independent components: 1. A mixed moving average component. 2. A harmonizable ...
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作者：Bernardin, C
作者单位：Universite Paris Saclay
摘要：We consider the simple asymmetric exclusion process with nonzero drift under the stationary Bernoulli product measure at density rho. We prove that for dimension d = 2 the occupation time of the site 0 is diffusive as soon as rho not equal 1/2. For dimension d = 1, if the density rho is equal to 1/2, we prove that the time t variance of the occupation time of the site 0 diverges in a certain sense at least as t(5/4).
