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作者：Kargin, Vladislav
作者单位：New York University
摘要：Let S-N be the sum of vector-valued functions defined on a finite Markov chain. An analogue of the Bemstein-Hoeffding inequality is derived for the probability of large deviations Of SN and relates the probability to the spectral gap of the Markov chain. Examples suggest that this inequality is better than alternative inequalities if the chain has a sufficiently large spectral gap and the function is high-dimensional.
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作者：Dupuis, Paul; Sezer, Ali Devin; Wang, Hui
作者单位：Brown University
摘要：Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of efficient importance sampling algorithms in the context of queueing networks. The standard approach, which simulates the system using an a priori fixed change of measure suggested by large deviation analysis, has been shown to fail in even the simplest network setting (e.g., a two-node tandem network). Exploiting connections between import...
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作者：Buraczewski, Dariusz
作者单位：University of Wroclaw
摘要：We consider an autoregressive model on R defined by the recurrence equation X-n = A(n)X(n-1) + B-n, where {(B-n, A(n))} are i.i.d. random variables valued in R x R+ and E[log A(1)] = 0 (critical case). It was proved by Babil-lot, Bougerol and Elie that there exists a unique invariant Radon measure of the process {X-n}. The aim of the paper is to investigate its behavior at infinity. We describe also stationary measures of two other stochastic recursions, including one arising in queuing theory.
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作者：Dong, Rui; Gnedin, Alexander; Pitman, Jim
作者单位：University of California System; University of California Berkeley; Utrecht University
摘要：Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process and observed that similar methods could be applied to more complex models. Mohle described the recursion which determines the generalization of the Ewens sampling formula in the situation where the lines of descent are governed by a Lambda-coalescent, which allows mu...
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作者：Caravenna, Francesco; Giacomin, Giambattista; Zambotti, Lorenzo
作者单位：University of Padua; Universite Paris Cite; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Sorbonne Universite
摘要：We consider a general model of a heterogeneous polymer chain fluctuating in the proximity of an interface between two selective solvents. The heterogeneous character of the model comes from the fact that the monomer units interact with the solvents and with the interface according to some charges that they carry. The charges repeat themselves along the chain in a periodic fashion. The main question concerning this model is whether the polymer remains tightly close to the interface, a phenomeno...
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作者：Bhatnagar, Nayantara; Caputo, Pietro; Tetali, Prasad; Vigoda, Eric
作者单位：University System of Georgia; Georgia Institute of Technology; Sapienza University Rome; University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：We study Markov chains which model genome rearrangements. These models are useful for studying the equilibrium distribution of chromosomal lengths, and are used in methods for estimating genomic distances. The primary Markov chain studied in this paper is the top-swap Markov chain. The top-swap chain is a card-shuffling process with n cards divided over k decks, where the cards are ordered within each deck. A transition consists of choosing a random pair of cards, and if the cards lie in diffe...
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作者：Elie, Romuald; Fermanian, Jean-David; Touzi, Nizar
作者单位：Institut Polytechnique de Paris; ENSAE Paris; BNP Paribas; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：Greek weight associated to a parameterized random variable Z(lambda) is a random variable pi such that del lambda E[phi(Z(lambda))] = E[phi(Z(lambda))pi] for any function phi. The importance of the set of Greek weights for the purpose of Monte Carlo simulations has been highlighted in the recent literature. Our main concern in this paper is to devise methods which produce the optimal weight, which is well known to be given by the score, in a general context where the density of Z(lambda) is no...
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作者：Bedard, Mylene
作者单位：University of Warwick
摘要：In this paper, we shall optimize the efficiency of Metropolis algorithms for multidimensional target distributions with scaling terms possibly depending on the dimension. We propose a method for determining the appropriate form for the scaling of the proposal distribution as a function of the dimension, which leads to the proof of an asymptotic diffusion theorem. We show that when there does not exist any component with a scaling term significantly smaller than the others, the asymptotically o...
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作者：Egloff, Daniel; Kohler, Michael; Todorovic, Nebojsa
摘要：Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in discrete time. Our approach is to recursively compute the so-called continuation values. They are defined as regression functions of the cash flow, which would occur over a series of subsequent time periods, if the approximated optimal exercise strategy is ...
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作者：Bertacchi, Daniela; Posta, Gustavo; Zucca, Fabio
作者单位：University of Milan; Polytechnic University of Milan
摘要：We study a generalized branching random walk where particles breed at a rate which depends on the number of neighboring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population survives without exploding. We construct a nontrivial invariant measure for this case.
