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作者：De Saporta, B; Yao, JF
作者单位：Universite de Rennes
摘要：Let Y be an Ornstein-Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X: dY(t) = a(X-t)Y-t dt + sigma (X-t) dW(t), Y-0 = y(0). Ergodicity conditions for Y have been obtained. Here we investigate the tail propriety of the stationary distribution of this model. A characterization of either heavy or light tail case is established. The method is based on a renewal theorem for systems of equations with distributions on R.
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作者：Alili, L; Kyprianou, AE
作者单位：University of Warwick; Utrecht University
摘要：The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Levy process and the solution of Gerber and Shiu [Astin Bull. 24 (1994) 195-220], Boyarchenko and Levendorskii [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J Control Optim. 40 (2002) 1663-1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and ...
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作者：Wagner, W
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：First we establish explosion criteria for jump processes with an arbitrary locally compact separable metric state space. Then these results are applied to two stochastic coagulation-fragmentation models-the direct simulation model and the mass flow model. In the pure coagulation case, there is almost sure explosion in the mass flow model for arbitrary homogeneous coagulation kernels with exponent bigger than 1. In the case of pure multiple fragmentation with a continuous size space, explosion ...
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作者：del Moral, P; Garnier, J
作者单位：Universite Cote d'Azur; Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Sorbonne Universite
摘要：In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Feynman-Kac path measures. The algorithmic implementation of the particle system is presented. An estimator for the probability of occurrence of a rare event is proposed and its variance is computed, which allows to compare and to optimize different versions of the algori...
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作者：Bovier, A; Faggionato, A
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
摘要：We review the aging phenomenon in the context of the simplest trap model, Bouchaud's REM-like trap model, from a spectral theoretic point of view. We show that the generator of the dynamics of this model can be diagonalized exactly. Using this result, we derive closed expressions for correlation functions in terms of complex contour integrals that permit an easy investigation into their large time asymptotics in the thermodynamic limit. We also give a grand canonical representation of the mode...
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作者：Mandjes, M; Van Uitert, M
作者单位：Centrum Wiskunde & Informatica (CWI); University of Twente; Vrije Universiteit Amsterdam
摘要：This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both nodes scaled appropriately, Schilder's sample-path large-deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower boun...
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作者：Baryshnikov, Y; Yukich, JE
作者单位：AT&T; Alcatel-Lucent; Lucent Technologies; Lehigh University
摘要：We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general results are used to deduce central limit theorems for measures induced by random graphs (nearest neighbor, Voronoi and sphere of influence graph), random sequential packing models (ballistic deposition and spatial birth-growth models) and statistics of germ...
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作者：Cheridito, P; Filipovic, D; Yor, M
作者单位：Princeton University; University of Munich; Universite Paris Cite; Sorbonne Universite
摘要：We provide explicit sufficient conditions for absolute continuity and equivalence between the distributions of two jump-diffusion processes that can explode and be killed by a potential.
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作者：Gobet, E; Lemor, JP; Warin, X
作者单位：Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; Electricite de France (EDF)
摘要：We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo simulations. A full convergence analysis is derived. Numerical experiments about finance are included, in particular, concerning option pricing with differential interest rates.
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作者：Berkes, I; Horváth, L; Kokoszka, P
作者单位：Graz University of Technology; Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Utah System of Higher Education; University of Utah; Utah System of Higher Education; Utah State University
摘要：Motivated by regularities observed in time series of returns on speculative assets, we develop an asymptotic theory of GARCH(1, 1) processes {y(k)} defined by the equations y(k) = sigmakepsilonk, sigma(k)(2) = omega + alphay(k-1)(2) + betasigma(k-1)(2) for which the sum a +,B approaches unity as the number of available observations tends to infinity. We call such sequences near-integrated. We show that the asymptotic behavior of near-integrated GARCH(1, 1) processes critically depends on the s...
