(Nonsymmetric) Dirichlet operators on L 1 : existence, uniqueness and associated Markov processes
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 1, pp. 99-140.
@article{ASNSP_1999_4_28_1_99_0,
     author = {Stannat, Wilhelm},
     title = {(Nonsymmetric) {Dirichlet} operators on $L^1$ : existence, uniqueness and associated {Markov} processes},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {99--140},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 28},
     number = {1},
     year = {1999},
     mrnumber = {1679079},
     zbl = {0946.31003},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1999_4_28_1_99_0/}
}
TY  - JOUR
AU  - Stannat, Wilhelm
TI  - (Nonsymmetric) Dirichlet operators on $L^1$ : existence, uniqueness and associated Markov processes
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1999
SP  - 99
EP  - 140
VL  - 28
IS  - 1
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1999_4_28_1_99_0/
LA  - en
ID  - ASNSP_1999_4_28_1_99_0
ER  - 
%0 Journal Article
%A Stannat, Wilhelm
%T (Nonsymmetric) Dirichlet operators on $L^1$ : existence, uniqueness and associated Markov processes
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1999
%P 99-140
%V 28
%N 1
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_1999_4_28_1_99_0/
%G en
%F ASNSP_1999_4_28_1_99_0
Stannat, Wilhelm. (Nonsymmetric) Dirichlet operators on $L^1$ : existence, uniqueness and associated Markov processes. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 1, pp. 99-140. http://archive.numdam.org/item/ASNSP_1999_4_28_1_99_0/

[ABR] S. Albeverio - V.I. Bogachev - M. Röckner, On uniqueness ofinvariant measures for finite and infinite dimensional diffusions, to appear in Comm. Pure Appl. Math. (1998). | MR | Zbl

[AKR1] S. Albeverio - YU.G. Kondratiev - M. Röckner, An approximate criterium of essential self-adjointness of Dirichlet operators, Potential Anal. 1 (1992), 307-317. | MR | Zbl

[AKR2] S. Albeverio - YU.G. Kondratiev - M. Röckner, Dirichlet operators via stochastic analysis, J. Funct. Anal. 128 (1995), 102-138. | MR | Zbl

[AR1] S. Albeverio - M. Röckner, Classical Dirichlet forms on topological vector spaces - Closability and a Cameron-Martin formula, J. Funct. Anal. 88 (1990), 395-436. | MR | Zbl

[AR2] S. Albeverio - M. Röckner, Dirichlet form methods for uniqueness of martingale problems and applications, in: "Stochastic Analysis". Proceedings of Symposia in Pure Mathematics, vol. 57 (1995), Am. Math. Soc. Rhode Island, 513-528. | MR | Zbl

[B] V.I. Bogachev, "Gaussian Measures", Mathematical Surveys and Monographs, vol. 62, AMS, Providence, 1998. | MR | Zbl

[BKR1] V.I. Bogachev - N. Krylov - M. Röckner, Regularity of invariant measures: the case of non-constant diffusion part, J. Funct. Anal. 138 (1996), 223-242. | MR | Zbl

[BKR2] V.I. Bogachev - N. Krylov - M. Röckner, Elliptic regularity and essential self-adjointness of Dirichlet operators on Rn, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 (1997), 451-461. | Numdam | MR | Zbl

[BH] N. Bouleau - F. Hirsch, "Dirichlet Forms and Analysis on Wiener space", Walter de Gruyter, Berlin, 1991. | MR | Zbl

[BR] V.I. Bogachev - M. Röckner, Regularity of invariant measures onfinite and infinite dimensional spaces and applications, J. Funct. Anal. 133 (1995), 168-223. | MR | Zbl

[Ca] E.A. Carlen, Stochastic mechanics of free scalar fields, "Stochastic mechanics and stochastic processes" (Swansea, 1986), Lecture Notes in Math. 1325, Springer, Berlin, (1988), 40-60. | MR | Zbl

[D1] E.B. Davies, "One-Parameter Semigroups", Academic Press, New York, 1980. | MR | Zbl

[D2] E.B. Davies, L1-Properties of second order elliptic operators, Bull. London Math. Soc. 17 (1985), 417-436. | MR | Zbl

[DeM] C. Dellacherie - P.-A. Meyer, "Probabilities and Potential C", North-Holland, Amsterdam, 1988. | MR | Zbl

[E] A. Eberle, Uniqueness and non-uniqueness of singular diffusion operators, Doctor degree thesis, Universität Bielefeld, 1998. | Zbl

[FOT] M. Fukushima - Y. Oshima - M. Takeda, "Dirichlet Forms and Symmetric Markov Processes", Walter de Gruyter, Berlin, 1994. | MR | Zbl

[Gr] L. Gross, Logarithmic Sobolev inequalities and contractivity properties of semigroups, in: G. DELL'ANTONIO, U. Mosco (Editors), " Dirichlet Forms", Lecture Notes in Mathematics 1563 (1992), Springer, Berlin. | MR | Zbl

[K] N.V. Krylov, "Lectures on Elliptic and Parabolic Equations in Hölder Spaces", Graduate Studies in Mathematics, vol. 12, American Mathematical Society, 1996. | MR | Zbl

[MR] Z.M. Ma - M. Röckner, "Introduction to the Theory of (Non-Symmetric) Dirichlet Forms", Berlin - Heidelberg - New York, Springer, 1992. | MR | Zbl

[Na] R. NAGEL (Editor), " One-parameter Semigroups of Positive Operators", Lecture Notes in Math. 1184, Springer, Berlin, 1986. | MR | Zbl

[Pa] A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations", Springer, Berlin, 1983. | MR | Zbl

[ReSi] M. Reed - B. Simon, "Methods of modem mathematical physics II. Fourier Analysis", Academic Press, New York - San Francisco - London, 1975. | MR | Zbl

[RSch] M. Röckner - B. Schmuland, Quasi-regular Dirichlet forms: examples and counterexamples, Canad. J. Math. (1) 47 (1995), 165-200. | MR | Zbl

[RZ] M. Röckner - T.S. Zhang, Uniqueness of generalized Schrödinger operators, Part II, J. Funct. Anal. 119 (1994), 455-467. | MR | Zbl

[Si] B. Simon, "The P (Φ)2 Euclidean (Quantum) field theory", Princeton University Press, Princeton, 1974. | Zbl

[S] K.- Th. Sturm, Analysis on local Dirichlet spaces, I. Recurrence, conservativeness and LP -Liouville properties, J. Reine Angew. Math. 456 (1994), 173-196. | MR | Zbl

[St1] W. Stannat, The theory of generalized Dirichlet forms and its applications in analysis and stochastics, SFB-343-Preprint 97-101, Bielefeld, to appear in Memoirs of the AMS (1997). | MR | Zbl

[St2] W. Stannat, First order perturbations of Dirichlet operators: existence and uniqueness, J. Funct. Anal. 141 (1996), 216-248. | MR | Zbl