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作者：Feng, Jin; Fouque, Jean-Pierre; Kumar, Rohini
作者单位：University of Kansas; University of California System; University of California Santa Barbara
摘要：In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear RIB-type equations where the fast variable lives in a noncompact space. We develop a general argument based on viscosity solutions which we apply to the two regimes studied in the paper. We derive a large deviation principle, and we deduce ...
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作者：Oshima, Kojiro; Techmann, Josef; Veluscek, Dejan
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Fujiwara's method can be considered as an extrapolation method of order 6 of the Ninomiya-Victoir weak approximation scheme for the numerical approximation of solution processes of SDEs. We present an extension of Fujiwara's method for arbitrarily high orders, which embeds the original Fujiwara method as the order 6 case. The approach can be considered as a variant of Richardson extrapolation, which allows one to reach high orders with few extrapolation steps. The most important contribution o...
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作者：Jenkins, Paul A.; Song, Yun S.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on asymptotic series has been introduced to make progress on this problem. Specifically, closed-form expressions have been derived for the first few terms in an asymptotic expansion of the two-locus sampling distribution when the recombination rate p is moderate to large. In this paper, a new computa...
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作者：Lanchier, Nicolas
作者单位：Arizona State University; Arizona State University-Tempe
摘要：This article is concerned with the Axelrod model, a stochastic process which similarly to the voter model includes social influence, but unlike the voter model also accounts for homophily. Each vertex of the network of interactions is characterized by a set of F cultural features, each of which can assume q states. Pairs of adjacent vertices interact at a rate proportional to the number of features they share, which results in the interacting pair having one more cultural feature in common. Th...
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作者：Yoshida, Nobuo
作者单位：Kyoto University
摘要：We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here, the extra stress tensor of the fluid is given by a polynomial of degree p - 1 of the rate of strain tensor, while the colored noise is considered as a random force. We focus on the shear thickening case, more precisely, on the case p is an element of [1 + d/2, 2d/d-2), where d is the dimension of the space. We prove t...
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作者：Decreusefond, Laurent; Dhersin, Jean-Stephane; Moyal, Pascal; Viet Chi Tran
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; IMT Atlantique; Centre National de la Recherche Scientifique (CNRS); Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Technologie de Compiegne; Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
摘要：We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The l...
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作者：Kang, Weining; Ramanan, Kavita
作者单位：University System of Maryland; University of Maryland Baltimore County; Brown University
摘要：A many-server queueing system is considered in which customers arrive according to a renewal process and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables. Customers enter service in the order of arrival and are assumed to abandon the queue if the waiting time in queue exceeds the patience time. The state of the system with N servers is represented by a four-component process that consists of the forward recur...
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作者：Tarres, Pierre; Vandekerkhove, Pierre
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：A device has two arms with unknown deterministic payoffs and the aim is to asymptotically identify the best one without spending too much time on the other. The Narendra algorithm offers a stochastic procedure to this end. We show under weak ergodic assumptions on these deterministic payoffs that the procedure eventually chooses the best arm (i.e., with greatest Cesaro limit) with probability one for appropriate step sequences of the algorithm. In the case of i.i.d. payoffs, this implies a que...
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作者：Bion-Nadal, Jocelyne; Kervarec, Magali
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Saclay
摘要：The framework of this paper is that of risk measuring under uncertainty which is when no reference probability measure is given. To every regular convex risk measure on C-b(Omega), we associate a unique equivalence class of probability measures on Borel sets, characterizing the riskless nonpositive elements of C-b(Omega). We prove that the convex risk measure has a dual representation with a countable set of probability measures absolutely continuous with respect to a certain probability measu...
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作者：Burnashev, Marat V.; Tchamkerten, Aslan
作者单位：Russian Academy of Sciences; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris
摘要：Given a Gaussian random walk (or a Wiener process), possibly with drift, observed through noise, we consider the problem of estimating its first-passage time tau(l) of a given level l with a stopping time eta defined over the noisy observation process. Main results are upper and lower bounds on the minimum mean absolute deviation in f(eta) E vertical bar eta - tau(l)vertical bar which become tight as l -> infinity. Interestingly, in this regime the estimation error does not get smaller if we a...
