Exponential Boundedness of Control Variables in a Sequentially Planned Bayesian Multiple Decision Problem in Continuous Time

In this article we study the exponential boundedness properties of certain specifically structured control variables in a finite sequentially planned Bayesian multiple decision problem in continuous time investigated by Roters (Roters, M. A sequentially planned Bayesian multiple decision problem in...

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Bibliographic Details
Published inSequential analysis Vol. 22; no. 4; pp. 347 - 358
Main Author Roters, Markus
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 31.12.2003
Subjects
AMS 1991 Subject Classification: Primary 62C10
Bayes procedure
Control variable
Martingale
Posterior distribution
Secondary 60G40
Termination properties
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Summary:In this article we study the exponential boundedness properties of certain specifically structured control variables in a finite sequentially planned Bayesian multiple decision problem in continuous time investigated by Roters (Roters, M. A sequentially planned Bayesian multiple decision problem in continuous time. Sequential Anal. 2002, 21, 59-86.). More precisely, we prove that the total sampling time, the number of observation stages und the total sampling cost associated with these control variables possess a moment generating function in a neighborhood of the origin. All these appealing properties hold for the optimal control variable found in Roters (Roters, M. A sequentially planned Bayesian multiple decision problem in continuous time. Sequential Anal. 2002, 21, 59-86.).
ISSN:0747-4946
1532-4176
DOI:10.1081/SQA-120026888