| 书目名称 | Stochastic Monotonicity and Queueing Applications of Birth-Death Processes | | 编辑 | E. A. Doorn | | 视频video | | | 丛书名称 | Lecture Notes in Statistics | | 图书封面 |  | | 描述 | A stochastic process {X(t): 0 S t < =} with discrete state space S c ~ is said to be stochastically increasing (decreasing) on an interval T if the probabilities Pr{X(t) > i}, i E S, are increasing (decreasing) with t on T. Stochastic monotonicity is a basic structural property for process behaviour. It gives rise to meaningful bounds for various quantities such as the moments of the process, and provides the mathematical groundwork for approximation algorithms. Obviously, stochastic monotonicity becomes a more tractable subject for analysis if the processes under consideration are such that stochastic mono tonicity on an inter val 0 < t < E implies stochastic monotonicity on the entire time axis. DALEY (1968) was the first to discuss a similar property in the context of discrete time Markov chains. Unfortunately, he called this property "stochastic monotonicity", it is more appropriate, however, to speak of processes with monotone transition operators. KEILSON and KESTER (1977) have demonstrated the prevalence of this phenomenon in discrete and continuous time Markov processes. They (and others) have also given a necessary and sufficient condition for a (temporally homogeneous) M | | 出版日期 | Book 1981 | | 关键词 | Geburts- und Todesprozess (Statistik); Markov chain; Markov process; Monotoner Operator; Warteschlange; b | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-5883-4 | | isbn_softcover | 978-0-387-90547-1 | | isbn_ebook | 978-1-4612-5883-4Series ISSN 0930-0325 Series E-ISSN 2197-7186 | | issn_series | 0930-0325 | | copyright | Springer-Verlag New York Inc. 1981 |
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发表于 2025-3-21 18:45:51
