Open Access Dissertation
Date of Award
We consider diffusions in two different contexts. First, we consider the so-called Feynman-Kac formula(s) for switching diffusions. These formulas provide stochastic representations for solutions of certain weakly coupled elliptical systems of partial differential equations. The formulas are verified for the boundary value problem, the initial value problem, and the initial boundary value problem. Second, we show the existence of near-optimal controls for a system driven by wideband noise in the presence of regime-switching. Using a relaxed control formulation, together with weak convergence methods, we show that given a stochastic optimal control problem, one may find a control that is near-optimal. The use of wideband noise is inspired from applications.
Baran, Nicholas, "On Switching Diffusions: The Feynman-Kac Formula And Near-Optimal Controls" (2014). Wayne State University Dissertations. 1042.