Stochastic Monotonicity and Queueing Applications of Birth-Death Processes
Doorn, Erik Van
ISBN 10: 0387905472 ISBN 13: 9780387905471
Published by Springer-Verlag New York Inc., 1981
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Series: Lecture Notes in Statistics. Num Pages: 124 pages, biography. BIC Classification: PBT. Category: (G) General (US: Trade). Dimension: 235 x 155 x 7. Weight in Grams: 201. . 1981. Softcover reprint of the original 1st ed. 1981. Paperback. . . . . Seller Inventory # V9780387905471
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).
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Title: Stochastic Monotonicity and Queueing ...
Publisher: Springer-Verlag New York Inc.
Publication Date: 1981
Binding: Soft cover
Condition: New
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Stochastic Monotonicity and Queueing Applications of Birth-Death Processes
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -A stochastic process {X(t): 0 S 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). 124 pp. Englisch. Seller Inventory # 9780387905471
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Stochastic Monotonicity and Queueing Applications of Birth-Death Processes
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Stochastic Monotonicity and Queueing Applications of Birth-Death Processes (Paperback)
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Paperback. Condition: new. Paperback. A stochastic process {X(t): 0 S 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 i}, i E S, are increasing (decreasing) with t on T. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780387905471
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Stochastic Monotonicity and Queueing Applications of Birth-Death Processes
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - A stochastic process {X(t): 0 S 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). Seller Inventory # 9780387905471
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