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Titlebook: Markov Chain Models — Rarity and Exponentiality; Julian Keilson Book 1979 Springer-Verlag New York Inc. 1979 Markov.Markov chain.Markowsch

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書目名稱Markov Chain Models — Rarity and Exponentiality
編輯Julian Keilson
視頻videohttp://file.papertrans.cn/625/624611/624611.mp4
叢書名稱Applied Mathematical Sciences
圖書封面Titlebook: Markov Chain Models — Rarity and Exponentiality;  Julian Keilson Book 1979 Springer-Verlag New York Inc. 1979 Markov.Markov chain.Markowsch
描述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 (§1.3, §2.4, §2.S) is important for many reasons. A) The only broad cla
出版日期Book 1979
關(guān)鍵詞Markov; Markov chain; Markowsche Kette; Random Walk; Sage; Variance; birth-death process; ergodicity; regene
版次1
doihttps://doi.org/10.1007/978-1-4612-6200-8
isbn_softcover978-0-387-90405-4
isbn_ebook978-1-4612-6200-8Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer-Verlag New York Inc. 1979
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Introduction and Summary,ation time distributions and their moments are of typical interest. Applications are oriented largely to reliability theory and inventory theory, but the methods apply as well to other branches of applied probability.
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The Fundamental Matrix, and Allied Topics,defined on the chain N(t). It also plays a key role in the central limit theorem for additive processes defined on the chain, in ergodic potential theory,. and in perturbation theory for Markov chains.
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Rarity and Exponentiality,g purposes, it is essential to quantify departure from exponentiality via error bounds. When one is dealing with time-reversible chains e.g., systems with independent Markov components, the complete monotonicity present permits such quantification and the error bounds needed.
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More on Time-Reversibility; Potential Coefficients; Process Modification,ion of time-reversibility to transient chains and “l(fā)ossy” chains. Time-reversible processes may be modified in a variety of ways without destroying the reversibility. The modified process is often of interest in its own right or is of primary interest. The last section introduces replacement processes, of special interest.
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