-
作者：Evans, SN
作者单位：University of California System; University of California Berkeley
摘要：We consider stochastic analogs of classical billiard systems. A particle moves at unit speed with constant direction in the interior of a bounded, d-dimensional region with continuously differentiable boundary. The boundary need not be connected; that is, the table may have interior obstacles. When the particle strikes the boundary, a new direction is chosen uniformly at random from the directions that point back into the interior of the region and the motion continues. Such chains are closely...
-
作者：Bovier, A; Mason, DM
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Delaware
摘要：We study a Hopfield model whose number of patterns M grows to infinity with the system size N, in such a way that M(N)(2) log M(N)IN tends to zero. In this model the unbiased Gibbs state in volume N can essentially be decomposed into M(N) pairs of disjoint measures. We investigate the distributions of the corresponding weights, and show, in particular, that these weights concentrate for any given N very closely to one of the pairs, with probability tending to 1. Our analysis is based upon a ne...
-
作者：Bank, P; Riedel, F
作者单位：Humboldt University of Berlin; Humboldt University of Berlin
摘要：We analyze the intertemporal utility maximization problem under uncertainty for the preferences proposed by Hindy, Huang and Kreps. Existence and uniqueness of optimal consumption plans are established under arbitrary convex portfolio constraints, including both complete and incomplete markets. For the complete market setting, we prove an infinite-dimensional version of the Kuhn-Tucker theorem which implies necessary and sufficient conditions for optimality. Using this characterization, we sho...
-
作者：Doytchinov, B; Lehoczky, J; Shreve, S
作者单位：Worcester Polytechnic Institute; Carnegie Mellon University; Carnegie Mellon University
摘要：This paper introduces a new aspect of queueing theory, the study of systems that service customers with specific timing requirements (e.g., due dates or deadlines). Unlike standard queueing theory in which common performance measures are customer delay, queue length and server utilization, real-time queueing theory focuses on the ability of a queue discipline to meet customer timing requirements, for example, the fraction of customers who meet their requirements and the distribution of custome...
-
作者：Borkovec, M; Klüppelberg, C
作者单位：Technical University of Munich
摘要：We consider the class of autoregressive processes with ARCH(1) errors given by the stochastic difference equation X-n = alphaX(n-1) + rootbeta + lambdaX(n-1)(2) epsilon(n), nis an element of N where (epsilon(n))(nepsilonN) are i.i.d. random variables, Under general and tractable assumptions we show the existence and uniqueness of a stationary distribution. We prove that the stationary distribution has a Paretu-like tail with a well-specified tail index which depends on alpha, lambda and the di...
-
作者：Khasminskii, RZ; Klebaner, FC
作者单位：Wayne State University; University of Melbourne
摘要：A stochastic analogue of the Lotka-Volterra model for predator-prey relationship is obtained when the birth rate of the prey and the death rate of the predator are perturbed by independent white noises with intensities of order epsilon (2), where epsilon > 0 is a small parameter. The evolution of this system is studied on large time intervals of O(1/epsilon (2)). It is shown that for small initial population sizes the stochastic model is adequate, whereas for large initial population sizes it ...
-
作者：Ignatiouk-Robert, I
作者单位：CY Cergy Paris Universite
摘要：In this paper we prove the local sample path large deviation estimates for a general class of Markov chains with discontinuous statistics. The local rate function is represented in terms of the convergence parameter of associated local transform matrices. Our method is illustrated by the case of perturbated random walks in Z(d).
-
作者：El Karoui, N; Peng, S; Quenez, MC
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Shandong University; Universite Gustave-Eiffel
摘要：This paper examines the continuous-time portfolio-consumption problem of an agent with a recursive utility in the presence of nonlinear constraints on the wealth. Using backward stochastic differential equations, we state a dynamic maximum principle which generalizes the characterization of optimal policies obtained by Duffie and Skiadas [J. Math Econ. 23, 107-131 (1994)] in the case of a linear wealth. From this property, we derive a characterization of optimal wealth and utility processes as...
-
作者：Bramson, M; Dai, JG
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：Using a slight modification of the framework of Bramson [7] and Williams [54], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single-station systems operating under first-in-first-out (FIFO), generalized-head-of-the-line proportional processor sharing (GHLPPS) and static buffer priority (SBP) service disciplines. The next two families are reentrant lines that operate under first-buffer-first-serve (FBFS) and last-buffer-firs...
-
作者：Mazza, C; Piau, D
作者单位：Universite Claude Bernard Lyon 1
摘要：We use McFadden's integral equations for random RC filters to study the average distribution of Dubins-Freedman processes. These distributions are also stationary probability measures of Markov chains on [0, 11, defined by the iteration of steps to the left x --> u x, and of steps to the right x - v + (1 - v) x, where u and v are random from [0, 1]. We establish new algorithms to compute the stationary measure of these chains. Turning to specific examples, we show that, if the distributions of...
