INVARIANCE OF CLOSED SETS UNDER STOCHASTIC CONTROL SYSTEMS

Introduction We are given two finite dimensional spaces H and H1, a complete probability space (Ω,F ,P), an increasing family of σ−sub-algebras Ft ⊂ F augmented by P−null sets of F and an H1-valued Ft-Brownian motion W (t), t ≥ 0 such that W (0) = 0.