Continuous-time Markov chains and applications : a by G. George Yin, Qing Zhang

By G. George Yin, Qing Zhang

Prologue and Preliminaries: advent and evaluate- Mathematical preliminaries.- Markovian models.- Two-Time-Scale Markov Chains: Asymptotic Expansions of strategies for ahead Equations.- profession Measures: Asymptotic houses and Ramification.- Asymptotic Expansions of ideas for Backward Equations.- Applications:MDPs, Near-optimal Controls, Numerical tools, and LQG with Switching: Markov choice Problems.- Stochastic keep watch over of Dynamical Systems.- Numerical tools for regulate and Optimization.- Hybrid LQG Problems.- References.- Index

Show description

Read or Download Continuous-time Markov chains and applications : a two-time-scale approach PDF

Similar operations research books

Factory Physics Second Edition

Accomplished creation to production administration textual content masking the habit legislation at paintings in factories. Examines working guidelines and strategic ambitions. Hopp provides the thoughts of producing approaches and controls inside a "physics" or "laws of nature" analogy--a novel strategy. there's adequate quantitative fabric for an engineer's path, in addition to narrative administration significant can comprehend and follow.

Expert Systems for Scanner Data Environments: The Marketing Workbench Laboratory Experience

This e-book is set the function of specialist platforms in advertising, fairly within the customer items undefined. part I describes the altering nature of purchaser advertising and provides the reason and want for professional structures. the rest of the booklet combines an academic on specialist platforms with a sequence of professional procedure prototypes.

Statistik und Ökonometrie für Wirtschaftswissenschaftler: Eine anwendungsorientierte Einführung

Das vorliegende Werk umfasst das gesamte statistische und ökonometrische Grundwissen, das für ein wirtschaftswissenschaftliches Studium benötigt wird. Verständlich und präzise werden an zahlreichen Beispielen die verschiedenen statistischen und ökonometrischen Herangehensweisen erklärt. Anhand verschiedenster Praxisfälle mit Musterlösungen und unter Einsatz der software program EViews und Excel werden die Inhalte greifbar, mittels zahlreicher Aufgaben wird die Anwendung des erlernten Wissens trainiert.

Additional resources for Continuous-time Markov chains and applications : a two-time-scale approach

Sample text

Our objective is to seek an approximation to the probability P (α(t) = k) with 0 ≤ k ≤ m. Denote p(t) = (P (α(t) = 0), . . , P (α(t) = m)). Then we have dp(t) = p(t)Q(t). 2) Considering the above problem, Massey and Whitt [157] introduced a small parameter ε > 0 to the generator Q(t). Assume that the rate of change of the generator Q(t) varies slowly in time that the process α(t) can achieve equilibrium before there is any significant change in the rate. Then we can replace Q(t) by Q(εt). In this replacement, we focus on α(t) in the neighborhood of time 0.

The idea of two-time-scale expansion has also found emerging applications in communication theory (see Tse, Gallager, and Tsitsiklis [206] among others). Parallel to the advances in the deterministic theory, there is a stochastic version of the averaging methods. It began with the work of Khasminskii [112], continued by the large deviations approach of Friedlin and Wentzell [67], and the martingale averaging methods of Kushner [139]. 12 1. Introduction and Overview In summary, the theories of Markov chains and singular perturbation have flourished.

One of the main ideas that underlies the basis of the asymptotic results throughout the book is the time-scale separation. 6. 7. 2 Birth and Death Processes In the study of physical and/or biological sciences, one needs to analyze the random evolution of a certain population. Its size (an integer-valued process) is a family of random variables {x(t) : t ≥ 0}. The reproduction and distinction of the population are conveniently modeled by assuming x(·) to be a Markov chain known as a birth and death process.

Download PDF sample

Rated 4.93 of 5 – based on 48 votes

Categories: Operations Research