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ABSTRACT
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.
Keywords:
- Bayes procedure
- Bellman equation
- Control variable
- Decision theory
- Discrete approximation
- Independent increments
- Markov property
- Martingale
- Optimal stopping
- Posterior distribution
- Sequentially planned decision procedure
- Stationary increments
- Homogeneous Markov system
- Stochastic process
- AMS 1991 Subject Classifications:
- Primary 62L15, 62C10
- Secondary 60G40, 60J25