-
作者：Mossel, Elchanan; Vigoda, Eric
作者单位：University of California System; University of California Berkeley; University System of Georgia; Georgia Institute of Technology
摘要：Markov chain Monte Carlo algorithms play a key role in the Bayesian approach to phylogenetic inference. In this paper, we present the first theoretical work analyzing the rate of convergence of several Markov chains widely used in phylogenetic inference. We analyze simple, realistic examples where these Markov chains fail to converge quickly. In particular, the data studied are generated from a pair of trees, under a standard evolutionary model. We prove that many of the popular Markov chains ...
-
作者：Araman, Victor F.; Glynn, Peter W.
作者单位：New York University; Stanford University
摘要：Consider a random walk S=(S-n:n >= 0) that is perturbed by a stationary sequence (xi(n): n >= 0) to produce the process (S-n+xi(n):n >= 0). This paper is concerned with computing the distribution of the all-time maximum M-infinity= max{S-k+xi(k):k >= 0) of perturbed random walk with a negative drift. Such a maximum arises in several different applications settings, including production systems, communications networks and insurance risk. Our main results describe asymptotics for P(M-infinity >...
-
作者：Clement, Emmanuelle; Kohatsu-Higa, Arturo; Lamberton, Damien
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University of Osaka
摘要：In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach considered here uses the properties of the linear equation satisfied by the error process. This methodology seems to apply to a large class of processes and we present as an example the weak approximation of stochastic delay equations.
-
作者：Hayes, Thomas P.; Vigoda, Eric
作者单位：University of California System; University of California Berkeley; University System of Georgia; Georgia Institute of Technology
摘要：We present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the stationary distribution to avoid worst-case configurations which arise in the traditional approach. As an application, we show that for k/Delta > 1.764, the Glauber dynamics on k-colorings of a graph on n vertices with maximum degree Delta converges in O (n log n) s...
-
作者：Chow, Pao-Liu
作者单位：Wayne State University
摘要：Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions. the existence theorem fora unique global solution is given. Next the questions of bounded solutions and the exponential stability of an equilibrium solution. in mean-square and the almost sure sense. are studied. Then. ...
-
作者：Devroye, Luc; Hwang, Hsien-Kuei
作者单位：McGill University; Academia Sinica - Taiwan
摘要：We propose a new, direct, correlation-free approach based on central moments of profiles to the asymptotics of width (size of the most abundant level) in some random trees of logarithmic height. The approach is simple but gives precise estimates for expected width, central moments of the width and almost sure convergence. It is widely applicable to random trees of logarithmic height, including recursive trees, binary search trees, quad trees, plane-oriented ordered trees and other varieties of...
-
作者：Klein, Irene
作者单位：University of Vienna
摘要：The main result of the paper is a version of the fundamental theorem of asset pricing (FTAP) for large financial markets based on an asymptotic concept of no market free lunch for monotone concave preferences. The proof uses methods from the theory of Orlicz spaces. Moreover, various notions of no asymptotic arbitrage are characterized in terms of no asymptotic market free lunch; the difference lies in the set of utilities. In particular, it is shown directly that no asymptotic market free lun...
-
作者：MacPhee, I. M.; Menshikov, M. V.; Popov, S.; Volkov, S.
作者单位：Durham University; University of Bristol; Universidade de Sao Paulo
摘要：We consider an exhaustive polling system with three nodes in its transient regime under a switching rule of generalized greedy type. We show that, for the system with Poisson arrivals and service times with finite second moment, the sequence of nodes visited by the server is eventually periodic almost surely. To do this, we construct a dynamical system, the triangle process, which we show has eventually periodic trajectories for almost all sets of parameters and in this case we show that the s...
-
作者：Neal, Peter; Roberts, Gareth
作者单位：University of Manchester; Lancaster University
摘要：[it this paper we shall consider optimal scaling problems for high-dimensional Metropolis-Hastings algorithms where updates call be chosen to be lower dimensional than the target density itself. We find that the optimal scaling rule for the Metropolis algorithm, Which tunes the overall algorithm acceptance rate to be 0.234. holds for the so-called Metropolis-within-Gibbs algorithm as well. Furthermore. the optimal efficiency obtainable is independent of the dimensionality of the update rule. T...
-
作者：Belhadji, L; Lanchier, N
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Minnesota System; University of Minnesota Twin Cities
摘要：Stochastic modeling of disease dynamics has had a long tradition. Among the first epidemic models including a spatial structure in the form of local interactions is the contact process. In this article we investigate two extensions of the contact process describing the course of a single disease within a spatially structured human population distributed in social clusters. That is, each site of the d-dimensional integer lattice is occupied by a cluster of individuals; each individual can be he...
