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作者：Kouritzin, MA; Long, HW
作者单位：University of Alberta
摘要：In the context of simulating the transport of a chemical or bacterial contaminant through a moving sheet of water, we extend a well-established method of approximating reaction-diffusion equations with Markov chains by allowing convection, certain Poisson measure driving sources and a larger class of reaction functions. Our alterations also feature dramatically slower Markov chain state change rates often yielding a ten to one-hundredfold simulation speed increase over the previous version of ...
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作者：Joyce, P; Krone, SM; Kurtz, TG
作者单位：University of Idaho; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：In this paper we consider large theta approximations for the stationary distribution of the neutral infinite alleles model as described by the the Poisson-Dirichlet distribution with parameter theta. We prove a variety of Gaussian limit theorems for functions of the population frequencies as the mutation rate theta goes to infinity. In particular, we show that if a sample of size n is drawn from a population described by the Poisson-Dirichlet distribution, then the conditional probability of a...
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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：Chow, PL
作者单位：Wayne State University
摘要：This paper is concerned with a class of nonlinear stochastic wave equations in R-d with d less than or equal to 3, for which the nonlinear terms are polynomial of degree m. As an example of the nonexistence of a global solution in general, it is shown that there exists an explosive solution of some cubically nonlinear wave equation with a noise term. Then the existence and uniqueness theorems for local and global solutions in Sobolev space H-1 are proven with the degree of polynomial m less th...
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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：Müller-Gronbach, T
作者单位：Technical University of Darmstadt
摘要：We analyze numerical methods for the pathwise approximation of a system of stochastic differential equations. As a measure of performance we consider the qth mean of the maximum distance between the solution and its approximation on the whole unit interval. We introduce an adaptive discretization that takes into account the local smoothness of every trajectory of the solution. The resulting adaptive Euler approximation performs asymptotically optimal in the class of all numerical methods that ...
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作者：Gromoll, HC; Puha, AL; Williams, RJ
作者单位：California State University System; California State University San Marcos; University of California System; University of California San Diego
摘要：Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps track of the residual service times of all jobs in the system at any given time. From this measure valued process, one can recover the traditional performance processes, including queue length and workload. We propose and study a critical fluid model (or forma...
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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.
