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

Bogachev VI, Krylov N, Röckner M (1996)
Journal of Functional Analysis 138(1): 223-242.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We prove regularity (i.e., smoothness) of measures mu on R(d) satisfying the equation L*mu = 0 where L is an operator of type Lu = tr(Au-'') + B . del u. Here A is a Lipschitz continuous, uniformly elliptic matrix-valued map and B is merely mu-square integrable. We also treat a class of corresponding infinite dimensional cases where R(d) is replaced by a locally convex topological vector space X. In this cases mu is proved to be absolutely continuous w.r.t. a Gaussian measure on X and the square root of the Radon-Nikodym density belongs to the Malliavin test function space D-2,D-1. (C) 1996 Academic Press. Inc.
Erscheinungsjahr
Zeitschriftentitel
Journal of Functional Analysis
Band
138
Ausgabe
1
Seite(n)
223-242
ISSN
PUB-ID

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Bogachev VI, Krylov N, Röckner M. Regularity of invariant measures: The case of non-constant diffusion part. Journal of Functional Analysis. 1996;138(1):223-242.
Bogachev, V. I., Krylov, N., & Röckner, M. (1996). Regularity of invariant measures: The case of non-constant diffusion part. Journal of Functional Analysis, 138(1), 223-242. doi:10.1006/jfan.1996.0063
Bogachev, V. I., Krylov, N., and Röckner, M. (1996). Regularity of invariant measures: The case of non-constant diffusion part. Journal of Functional Analysis 138, 223-242.
Bogachev, V.I., Krylov, N., & Röckner, M., 1996. Regularity of invariant measures: The case of non-constant diffusion part. Journal of Functional Analysis, 138(1), p 223-242.
V.I. Bogachev, N. Krylov, and M. Röckner, “Regularity of invariant measures: The case of non-constant diffusion part”, Journal of Functional Analysis, vol. 138, 1996, pp. 223-242.
Bogachev, V.I., Krylov, N., Röckner, M.: Regularity of invariant measures: The case of non-constant diffusion part. Journal of Functional Analysis. 138, 223-242 (1996).
Bogachev, Vladimir I., Krylov, N., and Röckner, Michael. “Regularity of invariant measures: The case of non-constant diffusion part”. Journal of Functional Analysis 138.1 (1996): 223-242.