Capacities, Measurable Selection and Dynamic Programming Part I: Abstract Framework

摘要

We give a brief presentation of the capacity theory and show how it derivesnaturally a measurable selection theorem following the approach of Dellacherie(1972). Then we present the classical method to prove the dynamic programmingof discrete time stochastic control problem, using measurable selectionarguments. At last, we propose a continuous time extension, that is an abstractframework for the continuous time dynamic programming principle (DPP).