Backward parabolic Ito equations and the second fundamental inequality
Nikolai Dokuchaev · Random Operators and Stochastic Equations · 2012
Abstract. Regularity of solutions is studied for backward stochastic parabolic Ito equations. An analog of the second fundamental inequality (second energy estimate) and the related existence theorem are obtained for domains with boundary. This result leads to a representation theorem for non-Markov processes in bounded domains and other applications.