Accretive Operators and Markov Decision Processes

The dynamic programming functional equation for an abstract, continuous parameter, Markov decision process is shown to involve an operator which is m-accretive, thus giving rise to a nonlinear semigroup, called the Bellman semigroup. A class of controls is specified for which the maximum expected reward over a finite planning horizon is given by this semigroup. This theory is applied to controlled jump, diffusion, and storage processes.