On Switching Diffusions: The Feynman-Kac Formula And Near-Optimal Controls
نویسندگان
چکیده
ON SWITCHING DIFFUSIONS: THEFEYNMAN-KAC FORMULA ANDNEAR-OPTIMAL CONTROLSbyNICHOLAS BARANAugust 2014Advisor: Dr. George YinMajor: MathematicsDegree: Doctor of Philosophy We consider diffusions in two different contexts. First, we consider the so-calledFeynman-Kac formula(s) for switching diffusions. These formulas provide stochasticrepresentations for solutions of certain weakly coupled elliptical systems of partialdifferential equations. The formulas are for the boundary value problem, the ini-tial value problem, and the initial boundary value problem. Second, we show theexistence of near-optimal controls for a system driven by wideband noise in the pres-ence of regime-switching. Using a relaxed control formulation, together with weakconvergence methods, we show that given a stochastic optimal control problem, onemay find a control that is near-optimal. The use of wideband noise is inspired byapplications.
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