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作者：FREIDLIN, MI; WENTZELL, AD
摘要：A number of asymptotic problems for ''classical'' stochastic processes leads to diffusion processes on graphs. In this paper we study several such examples and develop a general technique for these problems. Diffusion in narrow tubes, processes with fast transmutations and small random perturbations of Hamiltonian systems are studied.
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作者：EISENBAUM, N; KASPI, H
作者单位：Technion Israel Institute of Technology
摘要：Let X be a Markov process on an interval E of R, with lifetime zeta, admitting a local time at each point and such that P(x)(X hits y) > 0 for all x, y in E. We prove here that the local times process (L(zeta)x, x is-an-element-of E) is a Markov process if and only if X has fixed birth and death points and X has continuous paths. The sufficiency of this condition has been established by Ray, Knight and Walsh. The necessity is proved using arguments based on excursion theory. This result has be...
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作者：FALK, M; MAROHN, F
摘要：It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function F from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if F is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an iid sample, whether in terms of the distribution of the largest order ...
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作者：FONTES, LRG
摘要：For continuum 1/r2 Ising models, we prove that the critical value of the long range coupling constant (inverse temperature), above which an ordered phase occurs (for strong short range cutoff), is exactly 1. This leads to a proof of the existence of an ordered phase with slow decay of correlations. Our arguments involve comparisons between continuum and discrete Ising models, including (quenched and annealed) site diluted models, which may be of independent interest.
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作者：BAILLON, JB; CLEMENT, PH; GREVEN, A; DENHOLLANDER, F
作者单位：University of Gottingen; Delft University of Technology; Utrecht University
摘要：This paper considers an infinite system of particles on the integers Z that: (1) step to the right with a random delay, and (2) split or die along the way according to a random law depending on their position. The exponential growth rate of the particle density is computed in the long time limit in the form of a variational formula that can be solved explicitly. The result reveals two phase transitions associated with localization vs. delocalization and survival vs. extinction. In addition, th...
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作者：BORELL, C
摘要：Consider a convex domain B in R(n) and denote by p(t, x, y) the transition probability density of Brownian motion in B killed at the boundary of B. The main result in this paper, in particular, shows that the function s ln s(n)p(s2, x, y), (s, x, y) is-an-element-of R+ x B2, is concave.
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作者：PINSKY, RG
摘要：Let L generate a transient diffusion X(t) on R(d) and let D be an exterior domain. Let h be the smallest positive solution of Lh = 0 in D and h = 1 on partial derivative D. Define X(h)(t) to be the process X(t) conditioned to hit partial derivative D. By Doob's h-transform theory, X(h)(t) is also a Markov diffusion and its generator L(h) is defined by L(h)f = (1/h)L(hf). Letting tau(D) be the hitting time of partial derivative D, define the harmonic measure for X(h)(t) on partial derivative D ...
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作者：EIZENBERG, A; FREIDLIN, M
作者单位：University System of Maryland; University of Maryland College Park
摘要：We continue the study of the asymptotic behavior of Markov processes (X(epsilon)(t), v(epsilon)(t)) corresponding to systems of elliptic PDE with a small parameter epsilon > 0. In the present paper we consider the case where the process (X(epsilon)(t), v(epsilon)(t)) can leave a given domain D only due to large deviations from the degenerate process (X0(t), v0(t)). In this way we study the limit behavior of solutions of corresponding Dirichlet problems.
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作者：SUN, JY
摘要：This paper gives a general two-term approximation for the tail probability of the maxima of a class of differentiable Gaussian random fields and illustrates its potential statistical applications.
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作者：SLUD, EV
摘要：Let Y be a random variable defined by a polynomial p(W) of degree n in finitely many normally distributed variables. This paper studies which such variables Y are ''determinate,'' i.e., have probability laws uniquely determined by their moments. Extending results of Berg, which applied to powers of a single normal variable, we prove that (a) Y is determinate if n = 1, 2 or if n = 4, with the essential support of the law of Y strictly smaller than the real line, and (b) Y is not determinate eit...
