-
作者：Bansaye, Vincent; Delmas, Jean-Francois; Marsalle, Laurence; Tran, Viet Chi
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton-Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring locations depend on the position of the mother and the number of offspring. We prove a law of large numbers for the empirical measure of individuals alive at time t. This relies on a probabilistic interpretation of its intensity by mean of an auxiliary process. ...
-
作者：Chan, Hock Peng; Lai, Tze Leung
作者单位：National University of Singapore; Stanford University
摘要：Sequential Monte Carlo methods which involve sequential importance sampling and resampling are shown to provide a versatile approach to computing probabilities of rare events. By making use of martingale representations of the sequential Monte Carlo estimators, we show how resampling weights can be chosen to yield logarithmically efficient Monte Carlo estimates of large deviation probabilities for multidimensional Markov random walks.
-
作者：Chatterjee, Shirshendu; Durrett, Rick
作者单位：Cornell University; Duke University
摘要：Aldous [(2007) Preprint] defined a gossip process in which space is a discrete N x N torus, and the state of the process at time t is the set of individuals who know the information. Information spreads from a site to its nearest neighbors at rate 1/4 each and at rate N(-alpha) to a site chosen at random from the torus. We will be interested in the case in which alpha < 3, where the long range transmission significantly accelerates the time at which everyone knows the information. We prove thr...
