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作者：Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
作者单位：University of Munich; Princeton University; Goethe University Frankfurt
摘要：The Euler-Maruyama scheme is known to diverge strongly and numerically weakly when applied to nonlinear stochastic differential equations (SDEs) with superlinearly growing and globally one-sided Lipschitz continuous drift coefficients. Classical Monte Carlo simulations do, however, not suffer from this divergence behavior of Euler's method because this divergence behavior happens on rare events. Indeed, for such nonlinear SDEs the classical Monte Carlo Euler method has been shown to converge b...
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作者：Loh, Po-Shen; Lubetzky, Eyal
作者单位：Carnegie Mellon University; Microsoft
摘要：The following distributed coalescence protocol was introduced by Dahlia Malkhi in 2006 motivated by applications in social networking. Initially there are n agents wishing to coalesce into one cluster via a decentralized stochastic process, where each round is as follows: every cluster flips a fair coin to dictate whether it is to issue or accept requests in this round. Issuing a request amounts to contacting a cluster randomly chosen proportionally to its size. A cluster accepting requests is...
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作者：Schied, Alexander
作者单位：University of Mannheim
摘要：We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of J-functionals of Dawson-Watanabe superprocesses. This solution is related to the superprocess solution of quasilinear parabolic PDEs with singular terminal condition. For the probabilistic verification proof, we develop sharp bounds on the blow-up behavior of log-Laplace functionals of J-functionals, which might be of independent interest.
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作者：Dieker, A. B.; Gao, Xuefeng
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：We study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two regions of the state space, corresponding to overload (service demand exceeds capacity) and underload (service capacity exceeds demand). The two regimes cause standard techniques for proving positive recurrence to fail. Using and extending the framework of common...
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作者：Griffin, Philip S.
作者单位：Syracuse University
摘要：We investigate the behavior of Levy processes with convolution equivalent Levy measures, up to the time of first passage over a high level u. Such problems arise naturally in the context of insurance risk where u is the initial reserve. We obtain a precise asymptotic estimate on the probability of first passage occurring by time T. This result is then used to study the process conditioned on first passage by time T. The existence of a limiting process as u -> infinity is demonstrated, which le...
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作者：Kang, Hye-Won; Kurtz, Thomas G.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Wisconsin System; University of Wisconsin Madison
摘要：A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate choices of the exponents that can be applied to large complex networks. When the scaling implies subnetworks have different time-scales, the subnetworks can be approximated separately, providing insight into the behavior of the full network through the analysis...
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作者：Luczak, M. J.; Norris, J. R.
作者单位：University of London; University of Cambridge
摘要：We set out a general procedure which allows the approximation of certain Markov chains by the solutions of differential equations. The chains considered have some components which oscillate rapidly and randomly, while others are close to deterministic. The limiting dynamics are obtained by averaging the drift of the latter with respect to a local equilibrium distribution of the former. Some general estimates are proved under a uniform mixing condition on the fast variable which give explicit e...
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作者：Gamarnik, David; Goldberg, David A.
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University System of Georgia; Georgia Institute of Technology
摘要：We prove several results about the rate of convergence to stationarity, that is, the spectral gap, for the M/M/n queue in the Halfin-Whitt regime. We identify the limiting rate of convergence to steady-state, and discover an asymptotic phase transition that occurs w.r.t. this rate. In particular, we demonstrate the existence of a constant B* approximate to 1.85772 s.t. when a certain excess parameter B is an element of (0, B*], the error in the steady-state approximation converges exponentiall...
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作者：Latuszynski, Krzysztof; Roberts, Gareth O.; Rosenthal, Jeffrey S.
作者单位：University of Warwick; University of Toronto
摘要：We consider various versions of adaptive Gibbs and Metropolis-within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run by learning as they go in an attempt to optimize the algorithm. We present a cautionary example of how even a simple-seeming adaptive Gibbs sampler may fail to converge. We then present various positive results guaranteeing convergence of adaptive Gibbs samplers under certain conditions.
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作者：Hughes, Christopher; Najnudel, Joseph; Nikeghbali, Ashkan; Zeindler, Dirk
作者单位：University of York - UK; University of Zurich; University of Bielefeld
摘要：We consider a generalization of the Ewens measure for the symmetric group, calculating moments of the characteristic polynomial and similar multiplicative statistics. In addition, we study the asymptotic behavior of linear statistics (such as the trace of a permutation matrix or of a wreath product) under this new measure.
