Stochastic Convex Duality In L~p

This paper is concerned with the applications of general methods of convex analysis to problems of optimal stochastic control in the space of Lp for p>1. In particular we will define what dual problems are in optimal stochastic control, and what the coextremality conditions are for dual optimums. The methods and exposition of the results are very similar to the corresponding methods used by Rockafellar [5] and Bismut [2].In the last chapter of this paper, we will find applications of our conclusion in two problems of optimal stochastic control.