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作者：Sadowsky, John S.
作者单位：Arizona State University; Arizona State University-Tempe
摘要：Importance sampling is a Monte Carlo technique where random data are sampled from an alternative sampling distribution and an unbiased estimator is obtained by likelihood ratio weighting. Here we consider estimation of large deviations probabilities via importance sampling. Previous works have shown, for certain special cases, that exponentially twisted distributions possess a strong asymptotic optimality property as a sampling distribution. The results of this paper unify and generalize the p...
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作者：Kesten, Harry; Lee, Sungchul
作者单位：Cornell University; National University of Singapore
摘要：Let {X-i, 1 <= i < infinity} be i.i.d. with uniform distribution on [0, 1](d) and let M(X-1, . . . , X-n;alpha) be min{Sigma(e is an element of T') |e|(alpha); T' a spanning tree on {X-1, . . . , X-n;alpha) - EM(X-1, . . . , X-n}}. Then we show that for alpha > 0, [GRAPHIC] in distribution for some sigma(2)(alpha,d) > 0.
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作者：Cvitanic, Jaksa; Ma, Jin
作者单位：Columbia University; Purdue University System; Purdue University
摘要：In the classical continuous-time financial market model, stock prices have been understood as solutions to linear stochastic differential equations, and an important problem to solve is the problem of hedging options (functions of the stock price values at the expiration date). In this paper we consider the hedging problem not only with a price model that is nonlinear, but also with coefficients of the price equations that can depend on the portfolio strategy and the wealth process of the hedg...
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作者：Zhang, Q.; Yin, G.
作者单位：University System of Georgia; University of Georgia; Wayne State University
摘要：This work is concerned with the asymptotic properties of a singular perturbed nonstationary finite state Markov chain. In a recent paper of the authors, it was shown that as the fluctuation rate of the Markov chain goes to infinity, the probability distribution of the Markov chain converges to its time-dependent quasi-equilibrium distribution. In addition, asymptotic expansion of the probability distribution was obtained. This paper is a continuation of our effort in this direction. Upon using...
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作者：Yao, Yi-Ching; Simons, Gordon
作者单位：Colorado State University System; Colorado State University Fort Collins; Academia Sinica - Taiwan; University of North Carolina; University of North Carolina Chapel Hill
摘要：For an arbitrary point of a homogeneous Poisson point process in a d-dimensional Euclidean space, consider the number of Poisson points that have that given point as their rth nearest neighbor (r = 1, 2, ...). It is shown that as d tends to infinity, these nearest neighbor counts (r = 1, 2, ...) are iid asymptotically Poisson with mean 1. The proof relies on Renyi's characterization of Poisson processes and a representation in the limit of each nearest neighbor count as a sum of countably many...
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作者：Hsing, Tailen; Husler, Jurg; Reiss, Rolf-Dieter
作者单位：Texas A&M University System; Texas A&M University College Station; University of Bern; Universitat Siegen
摘要：Consider a triangular array of stationary normal random variables {xi(n,i), i >= 0, n >= 1} such that {xi(n,i), i >= 0} is a stationary normal sequence for each n >= 1. Let p(n,j) = corrq{xi(n,i), xi(n,i), (i + j) ). We show that if (1 - p(n),(j))log n -> delta(j) is an element of (0, infinity) as n -> infinity for some j, then the locations where the extreme values occur cluster, and if p(n,j) tends to 0 fast enough as j -> infinity for fixed n, then {xi(n,i), i >= 0} satisfies a certain weak...
