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作者：ARRATIA, R; TAVARE, S
摘要：The total variation distance between the process which counts cycles of size 1, 2,...,b of a random permutation of n objects and a process (Z1, Z2..... Z(b)) of independent Poisson random variables with EZ(i) = 1/i converges to 0 if and only if b/n --> 0. This Poisson approximation can be used to give simple proofs of limit theorems and bounds for a wide variety of functionals of random permutations. These limit theorems include the Erdos-Turin theorem for the asymptotic normality of the log o...
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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：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：NOLAN, JP
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作者：DINWOODIE, IH; ZABELL, SL
摘要：Say that a family (P(theta)n: theta is-an-element-of THETA) of sequences of probability measures is exponentially continuous if whenever theta(n) --> theta, the sequence {P(theta-n)n} satisfies a large deviation principle with rate function lambda(theta). If THETA is compact and {P(theta)n} is exponentially continuous, then the mixture P(n)(A) =: integral-THETA P(theta)n(A)d-mu(theta) satisfies a large deviation principle with rate function lambda(x) =: inf{lambda(theta)(x): theta is-an-elemen...
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作者：ALEXANDER, KS; KALIKOW, SA
摘要：Given a finite alphabet, there is an inductive method for constructing a stationary measure on doubly infinite words from this alphabet. This construction can be randomized; the main focus here is on a particular uniform randomization which intuitively corresponds to the idea of choosing a generic stationary process. It is shown that with probability 1, the random stationary process has zero entropy and gives positive probability to every periodic infinite word.
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作者：PENROSE, MD
摘要：We define a semi-min-stable (SMS) process Y(t) in [0, infinity) to be one which is stable under the simultaneous operations of taking the minima of n independent copies of Y(t) (pointwise over time t) and rescaling space and time. We show that the only possible rescaling of time is by a fixed power of n and that SMS processes are essentially the only possible weak limits for large m of a process obtained by taking the minimum, pointwise over t, of m independent copies of a given process and th...
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作者：LEE, TY
摘要：A branching diffusion process is studied when its diffusivity decreases to 0 at the rate of E much less than 1 and its branching/transmutation intensity increases at the rate of epsilon--1. We derive the action functionals which describe some large deviations of the processes as epsilon tends to 0. The branching diffusion processes are closely related to systems of semilinear parabolic differential equations.
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作者：ALSMEYER, G
摘要：Let X1, X2,... be i.i.d. random variables with common mean mu greater-than-or-equal-to 0 and associated random walk S0 = 0, S(n) = X1 + ... + X(n), n greater-than-or-equal-to 1. For a regularly varying function phi(t) = t(alpha)L(t), alpha > -1 with slowly varying L(t), we consider the generalized renewal function U(phi)(t) = SIGMA(n greater-than-or-equal-to 0) phi(n)P(S(n) less-than-or-equal-to t), t is-an-element-of R, by relating it to the family tau = tau(t) = inf{n greater-than-or-equal-t...
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作者：FLEMING, WH; JAMES, MR
作者单位：University of Kentucky
摘要：This paper is concerned with accurate asymptotic estimates for exit time probabilities associated with nearly deterministic Markov diffusions. The exit time probabilities are expressed as asymptotic series of WKB type in a small parameter, which measures the strength of the random Brownian motion inputs. This series is valid in certain regions in which the minimum action function u(x, s) is a smooth function of state x and time s. The function u is a solution to the cor-responding Hamilton-Jac...
