Regularity of invariant measures: The case of non-constant diffusion part

Journal of Functional Analysis

Volumn 138, Issue 1, 1996, Pages 223-242

  Bogachev, V I ^a   Krylov, N ^b   Rockner M ^c  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF MINNESOTA   (United States)

^c BIELEFELD UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030600930     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1996.0063     Document Type: Article

References (13)

1. [AR91] S. ALBEVERIO AND M. RÖCKNER, Stochastic differential equations in infinite dimensions: Solutions via Dirichlet forms, Probab. Theory Relat. Fields 89 (1991), 347-386.
2. [ARZ93] S. ALBEVERIO, M. RÖCKNER, AND T. S. ZHANG, Markov uniqueness for a class of infinite dimensional Dirichlet operators, in "Stochastic Processes and Optimal Control," (H. J. Engelbert et al., Eds.), Stochastic Monographs, Vol. 7, pp. 1-26, Gordon & Breach, New York, 1993.
3. [B93] V. I. BOGACHEV, Remarks on integration by parts in infinite dimensions, Acta Univ. Carolina 34 (1993), 11-29.
4. [BR94a] V. I. BOGACHEV AND M. RÖCKNER, Hypoellipticity and invariant measures of infinite-dimensional diffusions, C. R. Acad. Sci. Paris Ser. I 318 (1994), 553-558.
5. [BR94b] V. I. BOGACHEV AND M. RÖCKNER, Regularity of invariant measures on finite and infinite dimensional spaces and applications, J. Funct. Anal. 133 (1995), 168-223.
6. [BRZ95] V. I. BOGACHEV, M. RÖCKNER, AND T. S. ZHANG, manuscript in preparation.
7. [BS90] V. I. BOGACHEV AND O. G. SMOLYANOV, Analytic properties of infinite dimensional distributions, Russian Math. Surveys 45, No. 3 (1990), 1-104.
8. [G76] L. GROSS, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1976), 1061-1083.
9. [RZ92] M. RÖCKNER AND T. S. ZHANG, Uniqueness of generalized Schrödinger operators and applications, J. Funct. Anal. 105, No. 1 (1992), 187-231.
10. [RZ94] M. RÖCKNER AND T. S. ZHANG, Uniqueness of generalized Schrödinger operators, II, J. Funct. Anal. 119 (1994), 455-467.
11. [S70] E. STEIN, "Singular Integrals and Differentiability Properties of Functions," Princeton Univ. Press, Princeton, NJ, 1970.
12. [Sh87] I. SHIGEKAWA, Existence of invariant measures of diffusions on an abstract Wiener space, Osaka J. Math. 24, No. 1 (1987), 37-59.
13. [Ts77] B. S. TSIRELSON, Supplement to: A natural modification of a random process and its application to series of random functions and to Gaussian measures, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 72 (1977), 202-211.