Existence and Uniqueness of  Linear Equations Stemming from Optimal Control Problems

Martin Vieten
University of Wisconsin-Milwaukee
PhD Graduate Student

“Stockbridge et al. have developed a linear programming approach to stochastic control problems which originates from a formulation for the dynamics in form of martingale problem, together with a long-time average or discounted infinite horizon criterion. Recent research has put focus on a detailed investigation of the linear constraints of such problems, which are given by an operator-integral equation for so-called occupation measures.
Using standard ideas from differential equation solving and the classic construction of measures, I will show existence and uniqueness of certain linear constraints appearing in stochastic control. This is preceded by a short introduction to stochastic control, and an outline of how the presented results facilitate the use of numerical methods in control will conclude the talk”.