Duality and semi-group property for backward parabolic Ito equations

Details Duality and semi-group property for backward parabolic Ito equations Duality and semi-group property for backward parabolic Ito equations

2007-08-18

arxiv.org/abs/0708.2497v2

Random Operators and Stochastic Equations, 2010, V, 18, 51-72

Mathematics

Probability

Scientific paper

We study existence, uniqueness, semi-group property, and a priori estimates for solutions for backward parabolic Ito 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.

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