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作者：Ball, Frank; Brittont, Tom; Trapman, Pieter
作者单位：University of Nottingham; Stockholm University
摘要：Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size n. A Markovian SIR (susceptible -> infective -> recovered) infectious disease, having importation of infectives, taking place in this population is analysed. The main situation treated is where n -> infinity, keeping the basic reproduction number R-0 as well as the importation rate of infectives fixed, but assuming that the quotient of the avera...
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作者：Zhang, Li-Xin
作者单位：Zhejiang University
摘要：Stochastic approximation algorithms have been the subject of an enormous body of literature, both theoretical and applied. Recently, Laruelle and Pages [Ann. Appl. Probab. 23 (2013) 1409-1436] presented a link between the stochastic approximation and response-adaptive designs in clinical trials based on randomized urn models investigated in Bai and Hu [Stochastic Process. Appl. 80 (1999) 87-101; Ann. Appl. Probab. 15 (2005) 914-940], and derived the asymptotic normality or central limit theore...
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作者：Zhang, Tusheng
作者单位：University of Manchester
摘要：We introduce a discretization/approximation scheme for reflected stochastic partial differential equations driven by space time white noise through systems of reflecting stochastic differential equations. To establish the convergence of the scheme, we study the existence and uniqueness of solutions of Skorohod-type deterministic systems on time-dependent domains. We also need to establish the convergence of an approximation scheme for deterministic parabolic obstacle problems. Both are of inde...
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作者：Norris, James
作者单位：University of Cambridge
摘要：An explicit estimate is derived for Kac's mean-field model of colliding hard spheres, which compares, in a Wasserstein distance, the empirical velocity distributions for two versions of the model based on different numbers of particles. For suitable initial data, with high probability, the two processes agree to within a tolerance of order N-1/d, where N is the smaller particle number and d is the dimension, provided that d >= 3. From this estimate we can deduce that the spatially homogeneous ...
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作者：Foxall, Eric
作者单位：Arizona State University; Arizona State University-Tempe
摘要：We consider a stochastic model of infection spread incorporating monogamous partnership dynamics. In [Ann. AppL Probab. 26 (2016) 1297-1328], a basic reproduction number R-0 is defined with the property that if R-0 < 1 the infection dies out within O(log N) units of time, while if R-0 > 1 the infection survives for at least e(gamma N) units of time, for some gamma > 0. Here, we consider the critical case R-0 = 1 and show that the infection dies out within O (root N) units of time, and moreover...
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作者：Arlotto, Alessandro; Steele, J. Michael
作者单位：Duke University; University of Pennsylvania
摘要：We construct a stationary ergodic process X-1, X-2,... such that each X-t has the uniform distribution on the unit square and the length Ln of the shortest path through the points X-1, X-2,, X-n is not asymptotic to a constant times the square root of n. In other words, we show that the Beardwood, Halton, and Hammersley [Proc. Cambridge Philos. Soc. 55 (1959) 299-327] theorem does not extend from the case of independent uniformly distributed random variables to the case of stationary ergodic s...
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作者：Frikha, Noufel
作者单位：Universite Paris Cite
摘要：This paper studies multi-level stochastic approximation algorithms. Our aim is to extend the scope of the multi-level Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607-617] to the framework of stochastic optimization by means of stochastic approximation algorithm. We first introduce and study a two-level method, also referred as statistical Romberg stochastic approximation algorithm. Then its extension to a multi-level method is proposed. We prove a central limit theore...
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作者：Madaule, Thomas; Rhodes, Remi; Vargas, Vincent
作者单位：Universite Paris 13; Universite PSL; Universite Paris-Dauphine; Universite PSL; Ecole Normale Superieure (ENS)
摘要：In this paper, we consider the Gibbs measure associated to a logarithmically correlated random potential (including two-dimensional free fields) at low temperature. We prove that the energy landscape freezes and enters in the so-called glassy phase. The limiting Gibbs weights are integrated atomic random measures with random intensity expressed in terms of the critical Gaussian multiplicative chaos constructed in [Ann. Probab. 42 (2014) 1769-1808 and Comm. Math. Phys. (2013) To appear]. This c...
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作者：Narayanan, Hariharan
作者单位：University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle
摘要：We present a Markov chain, Dikin walk, for sampling from a convex body equipped with a self-concordant barrier. This Markov chain corresponds to a natural random walk with respect to a Riemannian metric defined using the Hessian of the barrier function. For every convex set of dimension n, there exists a self-concordant barrier whose self-concordance parameter is O (n). Consequently, a rapidly mixing Markov chain of the kind we describe can be defined (but not always be efficiently implemented...
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作者：Bertoin, Jean; Kortchemski, Igor
作者单位：University of Zurich
摘要：We are interested in the asymptotic behavior of Markov chains on the set of positive integers for which, loosely speaking, large jumps are rare and occur at a rate that behaves like a negative power of the current state, and such that small positive and negative steps of the chain roughly compensate each other. If X-n is such a Markov chain started at n, we establish a limit theorem for 1/n X-n appropriately scaled in time, where the scaling limit is given by a nonnegative self-similar Markov ...
