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作者：Bruss, FT; Ferguson, TS
作者单位：Universite Libre de Bruxelles; University of California System; University of California Los Angeles
摘要：How should we invest capital into a sequence of investment opportunities, if, for reasons of external competition, our interest focuses on trying to invest in the very best opportunity? We introduce new models to answer such questions. Our objective is to formulate them in a way that makes results high-risk specific in order to present true alternatives to other models. At the same time we try to keep them applicable in quite some generality, also for different utility functions. Viewing high-...
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作者：Jacka, S
作者单位：University of Warwick
摘要：We consider a model for the control of a satellite-fuel is expended in a linear fashion to move a satellite following a diffusion-the aim being to keep the satellite above a critical level. Under suitable assumptions on the drift and diffusion coefficients, it is shown that the probability of the satellite falling below the critical level is minimized by a policy that moves the satellite a certain distance above the critical level and then imposes a reflecting boundary at this higher level unt...
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作者：Solan, E; Vieille, N
作者单位：Northwestern University; Tel Aviv University; Hautes Etudes Commerciales (HEC) Paris
摘要：We address the problem of existence of the uniform value in recursive games. We give two existence results: (i) the uniform value is shown to exist if the state space is countable, the action sets are finite and if, for some a > 0, there are finitely many states in which the limsup value is less than a; (ii) for games with nonnegative payoff function, it is sufficient that the action set of player 2 is finite. The finiteness assumption can be further weakened.
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作者：Miclo, L
摘要：In 1999 Catoni determined the critical rate H-3 for the relaxation time of generalized Metropolis algorithms, models for which the speed of convergence to equilibrium can be strongly influenced by the effects of a possible almost periodicity. We recover this result with the help of Dobrushin's coefficient and give characterizations of H-3 in terms of other ergodic constants. In particular, we prove that it also governs the large deviation behavior of the singular gap for a sufficiently large b...
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作者：Bai, ZD; Hu, FF; Zhang, LX
作者单位：National University of Singapore; University of Virginia; Zhejiang University
摘要：We consider weak and strong Gaussian approximations for a two-color generalized Friedman's urn model with homogeneous and nonhomogeneous generating matrices. In particular, the functional central limit theorems and the laws of iterated logarithm are obtained. As an application, we obtain the asymptotic properties for the randomized-play-the-winner rule. Based on the Gaussian approximations, we also get some variance estimators for the urn model.
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作者：Berglund, N; Gentz, B
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Additive white noise may significantly increase the response of bistable systems to a periodic driving signal. We consider the overdamped motion of a Brownian particle in two classes of double-well potentials, symmetric and asymmetric ones. These potentials are modulated periodically in time with period 1/epsilon, where epsilon is a moderately (not exponentially) small parameter. We show that the response of the system changes drastically when the noise intensity sigma crosses a threshold valu...
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作者：Choi, KP; Xia, AH
作者单位：National University of Singapore; University of Melbourne
摘要：Let I-1, I-2, ..., I-n be independent Bernoulli random variables with P(I-i = 1) = 1 - P(I-i = 0) = p(i), 1 less than or equal to i less than or equal to n, and W = Sigma(i)(n) = (1) I-i, lambda = EW = Sigma(i)(n) = p(i). It is well known that if pi's are the same, then W follows a binomial distribution and if pi's are small, then the distribution of W, denoted by X W, can be well approximated by the Poisson(lambda). Define r = [lambda], the greatest integer less than or equal to lambda and se...
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作者：Cox, JT; Durrett, R
作者单位：Syracuse University; Cornell University
摘要：We study the stepping stone model on the two-dimensional torus. We prove several new hitting time results for random walks from which we derive some simple approximation formulas for the homozygosity in the stepping stone model as a function of the separation of the colonies and for Wright's genetic distance F-ST. These results confirm a result of Crow and Aoki (1984) found by simulation: in the usual biological range of parameters F-ST grows like the log of the number of colonies. In the othe...
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作者：Denuit, M; Müller, A
作者单位：Universite Catholique Louvain; Helmholtz Association; Karlsruhe Institute of Technology
摘要：The purpose of this paper is to show that many integral stochastic orders have a generator consisting of infinitely differentiable functions. This especially holds for all stochastic orders with characterizations via difference operators. The usefulness of this result is demonstrated in two applications relating to stochastic ordering of multivariate normal distributions and ordering of random vectors in a random environment.
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作者：Ma, J; Zhang, JF
作者单位：Purdue University System; Purdue University; University of Minnesota System; University of Minnesota Twin Cities
摘要：In this paper we investigate a class of backward stochastic differential equations (BSDE) whose terminal values are allowed to depend on the history of a forward diffusion. We first establish a probabilistic representation for the spatial gradient of the viscosity solution to a quasilinear parabolic PDE in the spirit of the Feynman-Kac formula, without using the derivatives of the coefficients of the corresponding BSDE. Such a representation then leads to a closed-form representation of the ma...
