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Girsanov’s theorem and ergodic properties of statistical solutions of nonlinear parabolic equations. (English. Russian original) Zbl 0684.60050

J. Sov. Math. 47, No. 3, 2547-2569 (1989); translation from Tr. Semin. Im. I. G. Petrovskogo 12, 88-117 (1987).
See the review in Zbl 0657.60080.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)

Citations:

Zbl 0657.60080
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References:

[1] M. I. Vishik, A. I. Komech, and A. V. Fursikov, ?Some mathematical problems of statistical hydromechanics,? Usp. Mat. Nauk,34, No. 5, 135?210 (1979). · Zbl 0503.76045
[2] T. V. Girya, ?Stabilization of statistical solutions of a nonlinear parabolic equations with white noise,? Usp. Mat. Nauk,36, No. 2, 177?178 (1981). · Zbl 0487.60054
[3] I. I. Gikhman (Gihman) and A. V. Skorokhod (Skorohod), The Theory of Stochastic Processes. I, Springer, New York (1974).
[4] I. I. Gikhman (Gihman) and A. V. Skorokhod (Skorohod), The Theory of Stochastic Processes. II, Springer, New York (1975).
[5] Yu. I. Daletskii and S. V. Fomin, Measures and Differential Equations in Infinite-Dimensional Spaces [in Russian], Nauka, Moscow (1983).
[6] I. V. Girsanov, ?On the transformation of a certain class of random processes by an absolutely continuous substitution of the measure,? Teor. Veroyatn. Primen.,5, No. 3, 314?330 (1960).
[7] E. Gagliardo, ?Proprieta di alcune classi di funzioni in piu variabili,? Ricerche Mat.,7, No. 1, 102?137 (1958). · Zbl 0199.44701
[8] J. L. Doob, Stochastic Processes, Wiley, New York (1953).
[9] R. S. Khas’minskii, Stability of Systems of Differential Equations under Random Perturbations of Their Parameters [in Russian], Nauka, Moscow (1969).
[10] J.-L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Nonlinéaires, Dunod, Gauthier-Villars, Paris (1969).
[11] H. Gajewski, K. Groger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operator-differentialgleichungem, Akademie-Verlag, Berlin (1974).
[12] M. I. Vishik and A. V. Fursikov, Mathematical Problems of Statistical Hydromechanics [in Russian], Nauka, Moscow (1980). · Zbl 0643.35005
[13] I. I. Gikhman (Gihman) and A. V. Skorokhod (Skorohod), The Theory of Stochastic Processes. III, Springers New York (1979).
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