Duality and semi-group property for backward parabolic Itô equations
Nikolai Dokuchaev · Random Operators and Stochastic Equations · 2010
Abstract We study existence, uniqueness, semi-group property and a-priori estimates for solutions of backward parabolic Itô equations in domains with boundary. We study also duality between forward and backward equations. The semi-group for backward equations is established in the form of some anti-causality. The novelty is that the semi-group property involves the diffusion term that is a part of the solution.