-
作者：Clancy, Damian
作者单位：University of Liverpool
摘要：We consider a stochastic model for the spread of an epidemic in a population split into m groups in which both infective and susceptible individuals are able to move between groups. Using a coupling argument similar to those applied to various other epidemic models by previous authors, we show that as the initial susceptible population becomes large, the process of infectives in this epidemic model converges to a multitype birth-and-death process with time-dependent birth rates. The behavior o...
-
作者：Dai, J. G.
作者单位：University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：This paper studies the instability of multiclass queueing networks. We prove that if a fluid limit model of the queueing network is weakly unstable, then the queueing network is unstable in the sense that the total number of customers in the queueing network diverges to in finity with probability 1 as time t -> infinity. Our result provides a converse to a recent result of Dai which states that a queueing network is positive Harris recurrent if a corresponding fluid limit model is stable. Exam...
-
作者：Bossy, Mireille; Talay, Denis
作者单位：Inria; Universite Cote d'Azur
摘要：In this paper we construct a stochastic particle method for the Burgers equation with a monotone initial condition; we prove that the convergence rate is O (1/root N + root Delta t. for the L-1 (R X Omega). norm of the error. To obtain that result, we link the PDE and the algorithm to a system of weakly interacting stochastic particles; the difficulty of the analysis comes from the discontinuity of the interaction kernel, which is equal to the Heaviside function. In a previous paper we showed ...
-
作者：Douglas, Jim, Jr.; Ma, Jin; Protter, Philip
作者单位：Purdue University System; Purdue University
摘要：In this paper we study numerical methods to approximate the adapted solutions to a class of forward-backward stochastic differential equations (FBSDE's). The almost sure uniform convergence as well as the weak convergence of the scheme are proved, and the rate of convergence is proved to be as good as the approximation for the corresponding forward SDE. The idea of the approximation is based on the four step scheme for solving such an FBSDE, developed by Ma, Protter and Yong. For the PDE part,...
-
作者：Takacs, Lajos
作者单位：University System of Ohio; Case Western Reserve University
摘要：This paper deals with the distribution function of the sojourn time of Brownian motion with drift. By some recent results of J. Akahori and A. Dassios this distribution function can be expressed in the form of a double integral. In this paper it is shown that the distribution function of the sojourn time can be expressed simply as a single integral. The result obtained is a generalization of the arc-sine law of Paul Levy.
-
作者：Berman, Simeon M.
摘要：Let (Xi, Y-i), i = 1, . . . , n, be independent random vectors with a standard bivariate normal distribution and let s(X) and s(Y) be the sample standard deviations. For arbitrary p, 0 < p < 1, define T-i = pX(i) + (1-p)Y-i and Z(i) = pX(i)/s(X) + (1-p)Y-i/s(Y,) i = 1, . . . ,n. The couple of pairs (T-i, Z(i)) and (T-j, Z(j)) is said to be discordant if either T-i < T-j and Z(i) > Z(j) or T-i > T-j and Z(i) < Z(j). It is shown that the expected number of discordant couples of pairs is asymptot...
-
作者：Kluppelberg, Claudia; Mikosch, Thomas
作者单位：Johannes Gutenberg University of Mainz; University of Groningen
摘要：Functionals of a two-parameter integrated periodogram have been used for detecting a change in the spectral distribution of a stationary sequence. The bases for these results are functional central limit theorems for the integrated periodogram with a Gaussian limit field. We prove functional central limit theorems for a general linear sequence having a finite fourth moment which is shown to be the optimal moment condition. Our approach is via an approximation of the integrated periodogram by a...
-
作者：Cerf, Raphael
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：Here is a new genetic algorithm. It is built by randomly perturbing a two operator crossover-selection scheme. Three conditions of biological relevance are imposed on the crossover. A new selection mechanism is used, which has the decisive advantage of preserving the diversity of the individuals in the population. The attractors of the unperturbed process are particular equi fitness subsets of populations endowed with a rich structure. The random vanishing perturbations are twofold: local pert...
