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作者：CHEN, LHY; CHOI, KP
摘要：Let X(n1),...,X(nn), n greater-than-or-equal-to 1, be independent random variables with P(X(ni) = 1) = 1 - P(X(ni) = 0) = p(ni) such that max{p(ni): 1 less-than-or-equal-to i less-than-or-equal-to n} --> 0 as n --> infinity. Let W(n) = SIGMA1 less-than-or-equal-to k less-than-or-equal-to n X(nk) and let Z be a Poisson random variable with mean lambda = EW(n). Poisson approximation for the distribution of W(n) dates back to 1960, when Le Cam obtained upper bounds for the total variation distanc...
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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...
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作者：ROSEN, J
作者单位：Technion Israel Institute of Technology
摘要：In this paper, we study a renormalized self-intersection local time for superprocesses over stable processes and classical diffusions. When the renormalization breaks down, we obtain limit theorems.
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作者：BARBOUR, AD; CHEN, LHY; LOH, WL
作者单位：National University of Singapore; Purdue University System; Purdue University
摘要：The aim of this paper is to extend Stein's method to a compound Poisson distribution setting. The compound Poisson distributions of concern here are those of the form POIS(v), where v is a finite positive measure on (0, infinity). A number of results related to these distributions are established. These in turn are used in a number of examples to give bounds for the error in the compound Poisson approximation to the distribution of a sum of random variables.
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作者：MILLET, A; NUALART, D; SANZ, M
作者单位：University of Barcelona
摘要：Consider the family of perturbed stochastic differential equations on R(d), X(t)e = X0e = square-root e integral-0/t sigma(X(s)e) . dW(s) + integral-0/t b(X(s)e) ds, e > 0, defined on the canonical space associated with the standard k-dimensional Wiener process W. We assume that {X0e, e > 0} is a family of random vectors not necessarily adapted and that the stochastic integral is a generalized Stratonovich integral. In this paper we prove large deviations estimates for the laws of {X.e, e > 0}...
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作者：MARQUES, MSD; MARTIN, LS
摘要：A sequence of measures on a topological space is pert-bed by a sequence of elements of a Lie group acting on that space. Criteria are given for the singularity and equivalence of the corresponding product measures. These criteria extend the results of Shepp and Steele. In particular, Fisher information comes into the scene and its role is further clarified.
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作者：ZAKAI, M; ZEITOUNI, O
摘要：Let {B, H, P0) be an abstract Wiener space and for every real rho, let T(rho)omega = omega + rho-F(omega) be a transformation from B to B. It is well known that under certain assumptions the measures induced by T(rho) or T(rho)-1 are mutually absolutely continuous with respect to P0 and the density function is represented by the Ramer formula. In this formula, the Carleman-Fredholm determinant det2(I(H) + rho-del-F) appears as a factor. We characterize the class of del-F for which a.s.-P0, det...
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作者：CHEN, D; LIGGETT, TM
作者单位：Peking University
摘要：In this article we propose and study finite reversible nearest particle systems in inhomogeneous and random environments. Using the Dirichlet principle and the ergodic theorem we prove that a finite reversible nearest particle system in a random environment determined by an i.i.d. sequence lambda(i) survives if E log lambda(i) > 0 and dies out if E-lambda(i) < 1. Some discussion is provided to show that both survival and extinction may happen when E log lambda(i) < 0 and E-lambda(i) > 1.
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作者：CATONI, O
摘要：Simulated annealing algorithms are time inhomogeneous controlled Markov chains used to search for the minima of energy functions defined on finite state spaces. The control parameters, the so-called cooling schedule, control the probability that the energy should increase during one step of the algorithm. Most of the studies on simulated annealing have dealt with limit theorems, such as characterizing convergence conditions on the cooling schedule, or giving an equivalent of the law of the pro...
