Stochastic Monotonicity and Queueing Applications of Birth-Death Processes (Lecture Notes in Statistics)

Doorn, Erik van

ISBN 10: 0387905472 / ISBN 13: 9780387905471

Published by Springer 12.03.1981., 1981

About this Item

128 Seiten ex Library Book Sprache: Englisch Gewicht in Gramm: 198 23,5 x 15,5 x 0,7 cm, Taschenbuch Auflage: Softcover reprint of the original 1st ed. 1981.

Seller Inventory # 355075

Bibliographic Details

• Title: Stochastic Monotonicity and Queueing Applications of Birth-Death Processes (Lecture Notes in Statistics)
• Publisher: Springer 12.03.1981.
• Publication Date: 1981
• Language: English
• ISBN 10: 0387905472
• ISBN 13: 9780387905471
• Binding: Soft cover
• Condition: Gut
• Seller catalogs:
  • Alle Bücher

About this title

Synopsis

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) Markov process to have monotone transition operators. Whether or not such processes will be stochas­ tically monotone as defined above, now depends on the initial state distribution. Conditions on this distribution for stochastic mono tonicity on the entire time axis to prevail were given too by KEILSON and KESTER (1977).