Regular, Sample Path and Strong Stochastic Convexity: A Review

Several notions of stochastic convexity and concavity and their properties are described in this survey. The notion of sample path stochastic convexity is a refinement of the well used notion of stochastic ordering, and it can be used to construct, on a common probability space, random variables whi...

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Veröffentlicht in:	Lecture Notes-Monograph Series. - Institute of Mathematical Statistics, 1982. - 19(1991) vom: Jan., Seite 320-333
1. Verfasser:	Shaked, Moshe (VerfasserIn)
Weitere Verfasser:	Shanthikumar, J. George
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	1991
Zugriff auf das übergeordnete Werk:	Lecture Notes-Monograph Series
Schlagworte:	Queueing theory Reliability theory Stochastic orderings Stochastic convexity Record values Branching processes Imperfect repair Mathematics Behavioral sciences Applied sciences


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100	1		\|a Shaked, Moshe \|e verfasserin \|4 aut
245	1	0	\|a Regular, Sample Path and Strong Stochastic Convexity: A Review
264		1	\|c 1991
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520			\|a Several notions of stochastic convexity and concavity and their properties are described in this survey. The notion of sample path stochastic convexity is a refinement of the well used notion of stochastic ordering, and it can be used to construct, on a common probability space, random variables which have desirable convexity (or concavity) properties with probability one. Three open problems from the literature are described. These problems could not be resolved until the introduction of the stochastic convexity notions which are described in this survey. The solutions of these problems illustrate the strength and the usefulness of these notions. Each notion is accompanied by a description of some of its applications. References for more detailed study of these notions are given. Indications of further work in this area are included.
540			\|a Copyright 1991 Institute of Mathematical Statistics
650		4	\|a Queueing theory
650		4	\|a Reliability theory
650		4	\|a Stochastic orderings
650		4	\|a Stochastic convexity
650		4	\|a Record values
650		4	\|a Branching processes
650		4	\|a Imperfect repair
650		4	\|a Mathematics \|x Pure mathematics \|x Geometry \|x Geometric properties \|x Convexity
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables
650		4	\|a Mathematics \|x Pure mathematics \|x Geometry \|x Geometric properties \|x Concavity
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Markov processes \|x Markov chains
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Probabilities
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Descriptive statistics \|x Statistical distributions \|x Distribution functions \|x Probability distributions \|x Continuous probability distributions \|x Density distributions \|x Reliability functions
650		4	\|a Behavioral sciences \|x Psychology \|x Cognitive psychology \|x Decision theory \|x Operations research \|x Queuing theory \|x Queueing networks
650		4	\|a Applied sciences \|x Systems science \|x Systems theory \|x Chaos theory
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Queueing theory
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Markov processes \|x Lectures and Speakers at the Workshop
655		4	\|a research-article
700	1		\|a Shanthikumar, J. George \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Lecture Notes-Monograph Series \|d Institute of Mathematical Statistics, 1982 \|g 19(1991) vom: Jan., Seite 320-333 \|w (DE-627)583817815 \|w (DE-600)2460925-0 \|x 07492170 \|7 nnns
773	1	8	\|g volume:19 \|g year:1991 \|g month:01 \|g pages:320-333
856	4	0	\|u https://www.jstor.org/stable/4355684 \|3 Volltext
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952			\|d 19 \|j 1991 \|c 01 \|h 320-333