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作者：Kollman, C; Baggerly, K; Cox, D; Picard, R
作者单位：National Marrow Donor Program; Rice University; United States Department of Energy (DOE); Los Alamos National Laboratory
摘要：In modeling particle transport through a medium, the path of a particle behaves as a transient Markov chain. We are interested in characteristics of the particle's movement conditional on its starting state, which take the form of a score accumulated with each transition. Importance sampling is an essential variance reduction technique in this setting, and we provide an adaptive (iteratively updated) importance sampling algorithm that converges exponentially to the solution. Examples illustrat...
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作者：Martin, JB; Suhov, YM
作者单位：Universite PSL; Ecole Normale Superieure (ENS); University of Cambridge; Russian Academy of Sciences
摘要：We extend the results of Vvedenskaya, Dobrushin and Karpelevich to Jackson networks. Each node j, 1 less than or equal to j less than or equal to J of the network consists of N identical channels, each with an infinite buffer and a single server with service rate mu(j) The network is fed by a family of independent Poisson flows of rates N lambda(1),...,N lambda(J) arriving at the corresponding nodes. After being served at node j, a task jumps to node k with probability p(jk) and leaves the net...
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作者：Fulman, J; Wilmer, EL
作者单位：Harvard University
摘要：The Poincare and Cheeger bounds are two useful bounds for the second largest eigenvalue of a reversible Markov chain. Diaconis and Stroock and Jerrum and Sinclair develop versions of these bounds which involve choosing paths. This paper studies these path-related bounds and shows that the Poincare bound is superior to the Cheeger bound for simple random walk on a tree and random walk on a finite group with any symmetric generating set. This partially resolves a question posed by Diaconis and S...
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作者：Pittel, B
作者单位：University System of Ohio; Ohio State University
摘要：For various global characteristics of large ge size combinatorial structures, such as graphs, trees, one can usually estimate the mean and the variance, and also obtain a recurrence for the generating function, with the structure size n serving as the recursive parameter As a heuristic principle based on our experience, we claim that such a characteristic is asymptotically normal if the mean and the variance are nearly linear in n. The technical reason is that in such a case the moment generat...
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作者：Frieze, A; Kannan, R
作者单位：Carnegie Mellon University; Carnegie Mellon University
摘要：We consider the problem of sampling according to a distribution with log-concave density F over a convex body K subset of or equal to R-n. The sampling is done using a biased random walk and we give improved polynomial upper bounds on the time to get a sample point with distribution close to F.
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作者：Brooks, EA
作者单位：National Institutes of Health (NIH) - USA; NIH National Institute of Environmental Health Sciences (NIEHS)
摘要：Linear reaction-hyperbolic systems of partial differential equations in one space dimension arise in the study of the physiological process by which materials are transported in nerve cell axons. Probabilistic methods are developed to derive a closed form approximate solution for an initial-boundary value problem of such a system. The approximate solution obtained is a translating solution of a heat equation. An estimate is proved giving the deviation of this approximate traveling wave solutio...
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作者：Biskup, M; den Hollander, F
作者单位：Radboud University Nijmegen; Charles University Prague
摘要：We consider a quenched-disordered heteropolymer, consisting of hydrophobic and hydrophylic monomers, in the vicinity of an oil-water interface. The heteropolymer is modeled by a directed simple random walk (i, S-i)(i is an element of N) on N x Z with an interaction given by the Hamiltonians H-n(omega)(S) = lambda Sigma(i=1)(n)(omega(i) + h)Sign(S-i) (n is an element of N). Here, lambda and h are parameters and (omega(i))(i is an element of N) are i.i.d. ii-valued random variables. The sign(S-i...
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作者：Khoshnevisan, D; Lewis, TM
作者单位：Utah System of Higher Education; University of Utah
摘要：In this paper, we give a pathwise development of stochastic integrals with respect to iterated Brownian motion. We also provide a detailed analysis of the variations of iterated Brownian motion. These variations are linked to Brownian motion in random scenery and iterated Brownian motion itself.
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作者：Kramkov, D; Schachermayer, W
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Technische Universitat Wien; University of Vienna
摘要：The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less than 1.
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作者：Freidlin, M; Weber, M
作者单位：University System of Maryland; University of Maryland College Park; Technische Universitat Dresden
摘要：We describe the long-time behavior of the nonlinear pendulum perturbed by a small noise. To derive this asymptotics, one has to consider diffusion processes on the graph corresponding to the Hamiltonian of the pendulum.
