A SEQUENTIALLY PLANNED BAYESIAN MULTIPLE DECISION PROBLEM IN CONTINUOUS TIME

In this paper we formulate a finite sequentially planned Bayesian multiple decision problem, thereby introducing a theory of optimal sampling for stochastic processes in continuous time as an alternative observation concept to stopping times, and elaborate the existence and the structure of a Bayes...

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Bibliographic Details
Published inSequential analysis Vol. 21; no. 1-2; pp. 59 - 86
Main Author Roters, Markus
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 20.05.2002
Subjects
AMS 1991 Subject Classifications
Bayes procedure
Bellman equation
Control variable
Decision theory
Discrete approximation
Homogeneous Markov system
Independent increments
Markov property
Martingale
Optimal stopping
Posterior distribution
Primary 62L15, 62C10
Secondary 60G40, 60J25
Sequentially planned decision procedure
Stationary increments
Stochastic process
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ISSN0747-4946
1532-4176
DOI10.1081/SQA-120004173

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Summary:In this paper we formulate a finite sequentially planned Bayesian multiple decision problem, thereby introducing a theory of optimal sampling for stochastic processes in continuous time as an alternative observation concept to stopping times, and elaborate the existence and the structure of a Bayes procedure for the sequentially planned observation of stochastic processes of the exponential class. The optimal procedure consists of a Bayesian terminal decision procedure (non-sequential part) and an optimal control variable (sequential part). Moreover, some properties of the Bayes procedure are considered.
ISSN:0747-4946
1532-4176
DOI:10.1081/SQA-120004173