Markov Chain Models - Rarity and Exponentiality

Language: English

Published by Humana, 1979

0387904050 / 9780387904054

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nach der Bestellung gedruckt Neuware - Printed after ordering - in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly.O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains by a uniformizing procedure (2.l) that simplifies and unifies the theory and enables results for discrete and continuous time to be discussed simultaneously. Thus if N(t) is any finite Markov chain in continuous time governed by transition rates vmn one may write for pet) = [Pmn(t)] - P[N(t) = n I N(O) = m] pet) = exp [-vt(I - a )] (0.1.1) v where v > Max r v ' and mn m n law ~ 1 - v-I \* Hence N(t) where is governed r vmn Nk = NK(t) n K(t) is a Poisson process of rate v indep- by a ' and v dent of N - k Time-reversibility (1.32.42.S) is important for many reasons. A) The only broad class of tractable chains suitable for stochastic models is the time-reversible class. …

Seller Inventory # 9780387904054

Title
Markov Chain Models - Rarity and Exponentiality
Author
J. Keilson
Publisher
Humana
Publication year
1979
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
0387904050
ISBN 13
9780387904054
Item weight
318 grams
Dimensions
235x155x12 mm

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