A Stochastic Control Approach to a Parabolic Equation, Reciprocal Processes

2000 Mathematics Subject Classi cation: 49L60, 60J60, 93E20.

A controllability problem for a Fokker-Planck equation is considered. A solution (v*, ф*) to that problem is constructed by a theorem of Jamison, under proper assumptions. We give a sufficiency condition concerning the initial and terminal data for that solution to exist. We show that v* is an optimal feedback control for a stochastic optimal control problem. Further, we prove that the corresponding optimally controled stochastic process is a reciprocal process which is Markov.