The Annals of Probability

Decision Processes with Total-Cost Criteria

Stephen Demko and Theodore P. Hill

Full-text: Open access


By a decision process is meant a pair $(X, \Gamma)$, where $X$ is an arbitrary set (the state space), and $\Gamma$ associates to each point $x$ in $X$ an arbitrary nonempty collection of discrete probability measures (actions) on $X$. In a decision process with nonnegative costs depending on the current state, the action taken, and the following state, there is always available a Markov strategy which uniformly (nearly) minimizes the expected total cost. If the costs are strictly positive and depend only on the current state, there is even a stationary strategy with the same property. In a decision process with a fixed goal $g$ in $X$, there is always a stationary strategy which uniformly (nearly) minimizes the expected time to the goal, and, if $X$ is countable, such a stationary strategy exists which also (nearly) maximizes the probability of reaching the goal.

Article information

Ann. Probab., Volume 9, Number 2 (1981), 293-301.

First available in Project Euclid: 19 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 60G99: None of the above, but in this section
Secondary: 62C05: General considerations

Gambling theory dynamic programming decision theory stationary strategy Markov strategy total-cost criteria


Demko, Stephen; Hill, Theodore P. Decision Processes with Total-Cost Criteria. Ann. Probab. 9 (1981), no. 2, 293--301. doi:10.1214/aop/1176994470.

Export citation