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作者：DAY, MV
摘要：The small noise exit problem of Wentzell and Freidlin is of particular interest for regions whose boundary consists of trajectories of the underlying (unperturbed) dynamical system. This is called the case of characteristic boundary. One fruitful approach to attacking this problem involves conditioning the probability measure so that exit to the boundary occurs more quickly. In a previous paper, this approach was applied to some simplified examples, revealing some previously unanticipated phen...
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作者：DYNKIN, EB
摘要：We establish connections between superdiffusion processes and one class of nonlinear parabolic differential equations. Analytic results due to Brezis and Friedman, Baras and Pierre and others are used to investigate the graphs of superdiffusions. A survey of the literature and general comments are presented in Section 4.
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作者：KHOSHNEVISAN, D
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We briefly show an extension of inequalities of Burkholder and Gundy for linear Brownian motion to certain monotone functionals of the d-dimensional Brownian convex hull. Our results belong to a class of results that imply that Brownian hulls are much like the one-dimensional maximal process.
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作者：LIGGETT, TM
摘要：Consider the inhomogeneous contact process on Z1 with recovery rate delta(k) at site k and infection rates lambda(k) and rho(k) at site k due to the presence of infected neighbors at k - 1 and k + 1 respectively. A special case of the main result in this paper is the following: Suppose that the environment is chosen in such a way that the delta(k)'s, lambda(k)'s and rho(k)'s are all mutually independent, with the delta(k)'s having a common distribution, and the lambda(k)'s and rho(k)'s having ...
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作者：BRYDGES, D; EVANS, SN; IMBRIE, JZ
作者单位：University of California System; University of California Berkeley; Harvard University; Harvard University
摘要：We define a Levy process on a d-dimensional hierarchical lattice. By construction the Green's function for this process decays as \x\2-d . For d = 4, we prove that the introduction of a sufficiently weak self-avoidance interaction does not change this decay provided the mass = killing rate is chosen in a special way, so that the process is critical.
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作者：FINNER, H
摘要：The main result of this article is a generalization of the generalized Holder inequality for functions or random variables defined on lower-dimensional subspaces of n-dimensional product spaces. It will be seen that various other inequalities are included in this approach. For example, it allows the calculation of upper bounds for the product measure of n-dimensional sets with the help of product measures of lower-dimensional marginal sets. Furthermore, it yields an interesting inequality for ...
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作者：FISCH, R
摘要：This paper investigates the dynamics of the one-dimensional three-color cyclic cellular automaton. The author has previously shown that this process fluctuates, meaning that each lattice site changes color infinitely often, so that there is no final state for the system. The focus of the current work is on the clustering properties of this system. This paper demonstrates that the one-dimensional three-color cyclic cellular automaton clusters, and the mean cluster size, as a function of time t,...
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作者：DALANG, RC; WALSH, JB
作者单位：University of British Columbia
摘要：This paper examines the question of when a two-parameter process X of independent increments will have Levy's sharp Markov property relative to a given domain D. This property states intuitively that the values of the process inside D and outside D are conditionally independent given the values of the process on the boundary of D. Under mild assumptions, X is the sum of a continuous Gaussian process and an independent jump process. We show that if X satisfies Levy's sharp Markov property, so d...
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作者：SCHINAZI, R
摘要：We apply an invariance principle due to De Masi, Ferrari, Goldstein and Wick to the edge process for critical reversible nearest-particle systems. Their result also gives an upper bound for the diffusion constant that we compute explicitly. A comparison between the movement of the edge, when the other particles are frozen, and a random walk allows us to find a lower bound for the diffusion constant. This shows that the right renormalization for the edge to converge to a nondegenerate Brownian ...
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作者：NOLAN, JP
