Girsanov's theorem and ergodic properties of statistical solutions of nonlinear parabolic equations

Theorems on the existence and uniqueness of the statistical solutions and for the existence of stationary solutions for nonlinear stochastic equations are proved. Markov families of statistical solutions are constructed. The ergodic properties of monotone systems are investigated. A Girsanov type theorem on the absolute continuity of the statistical solution of a nonlinear stochastic parabolic equation with respect to the statistical solution of the monotone equation is proved.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 12, pp. 88–117, 1987.