Duality and semi-group property for backward parabolic Ito equations.
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Dokuchaev, Nikolai. 2010. Duality and semi-group property for backward parabolic Ito equations. Random Operators and Stochastic Equations. 18: pp. 51-72.
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Random Operators and Stochastic Equations
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School of Science and Computing
Department of Mathematics and Statistics
Faculty of Science and Engineering
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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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