| 书目名称 | Markov Chain Models — Rarity and Exponentiality |
| 编辑 | Julian Keilson |
| 视频video | |
| 丛书名称 | Applied Mathematical Sciences |
| 图书封面 |  |
| 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 |
| 关键词 | Markov; Markov chain; Markowsche Kette; Random Walk; Sage; Variance; birth-death process; ergodicity; regene |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-1-4612-6200-8 |
| isbn_softcover | 978-0-387-90405-4 |
| isbn_ebook | 978-1-4612-6200-8Series ISSN 0066-5452 Series E-ISSN 2196-968X |
| issn_series | 0066-5452 |
| copyright | Springer-Verlag New York Inc. 1979 |
发表于 2025-3-21 18:35:07
