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General theory of Dirichlet forms and applications

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Dirichlet Forms

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References

  1. Airault, H., Van Biesen, J.: Le processus d'Ornsteïn-Uhlenbeck sur une sous-variété de l'espace de Wiener. Bull. Sc. math., 2e série, t. 115 (1991), 185–210.

    MATH  Google Scholar 

  2. Airault, H., Malliavin, P.: Intégration géométrique sur l'espace de Wiener. Bull. Sc. math., 2e série, t. 112 (1988), 3–52.

    MathSciNet  MATH  Google Scholar 

  3. Albeverio, S., Brasche, J., Röckner, M.: Dirichlet forms and generalized Schrödinger operators. In: Proc. Summer School Schrödinger operators, ed. H. Holden and A. Jensen. Lecture Notes in Physics 345, 1–42. Berlin: Springer 1989.

    Chapter  Google Scholar 

  4. Albeverio, S., Kusuoka, S., Röckner, M.: On partial integration in infinite dimensional space and applications to Dirichlet forms. J. London Math. Soc. 42, 122–136 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  5. Albeverio, S. Leandre, R., Röckner, M.: Construction of a rotational invariant diffusion on the free loop space. Preprint (1992). Publication in preparation.

    Google Scholar 

  6. Albeverio, S., Ma, Z.M., Röckner, M.: A Beurling-Deny type structure theorem for Dirichlet forms on general state space. To appear in: Memorial Volume for R. Høegh-Krohn.

    Google Scholar 

  7. Albeverio, S., Ma, Z.M., Röckner, M.: Non-symmetric Dirichlet forms and Markov processes on general state space. C.R. Acad. Sci. Paris, t. 314, Série I, 77–82 (1992).

    MathSciNet  MATH  Google Scholar 

  8. Albeverio, S., Ma., Z.M., Röckner, M.: Regularization of Dirichlet spaces and applications. To appear in C.R. Acad. Sci. Paris, Série I, (1992).

    Google Scholar 

  9. Albeverio, S., Ma, Z.M., Röckner, M.: Local property of Dirichlet forms and diffusions on general state spaces. Preprint (1992). Publication in preparation.

    Google Scholar 

  10. Albeverio, S., Ma, Z.M., Röckner, M.: Characterization of (nonsymmetric) Dirichlet forms associated with Hunt processes. Preprint (1992). Publication in preparation.

    Google Scholar 

  11. Albeverio, S., Röckner, M.: Dirichlet forms, quantum fields and stochastic quantization. In: Stochastic analysis, path integration, and dynamics. Research Notes in Math. 200, 1–21. Editors: K.D. Elworthy, J.C. Zambrini, Harlow: Longman 1989.

    Google Scholar 

  12. Albeverio, S., Röckner, M.: Classical Dirichlet forms on topological vector spaces-construction of an associated diffusion process. Probab. Th. Rel. Fields 83, 405–434 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  13. Albeverio, S., Röckner, M.: Classical Dirichlet forms on topological vector spaces-closability and a Cameron-Martin formula. J. Funct. Anal. 88, 395–436 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  14. Albeverio, S., Röckner, M.: New developments in the theory and application of Dirichlet forms. In: Stochastic processes, physics and geometry, 27–76, Ascona/Locarno, Switzerland, 4–9 July 1988, Editors: S. Albeverio et al., Singapore: World Scientific 1990.

    Google Scholar 

  15. Albeverio, S., Röckner, M.: Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms. Probab. Th. Rel. Fields 89, 347–386 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  16. Albeverio, S., Röckner, M., Zhang, T.S.: Girsanov transform for symmetric diffusions with infinite dimensional state space. Preprint (1991). Ann. Prob., in press.

    Google Scholar 

  17. Badrikian, A.: Séminaire sur les fonctions aléatoires linéaires et les measures cylindriques. Lecture Notes in Math. 139. Berlin: Springer 1970.

    Book  MATH  Google Scholar 

  18. Beurling, A., Deny, J.: Espaces de Dirichlet. Acta Math. 99, 203–224 (1958).

    Article  MathSciNet  MATH  Google Scholar 

  19. Beurling, A., Deny, J.: Dirichlet spaces. Proc. Nat. Acad. Sci. U.S.A. 45, 208–215 (1959).

    Article  MathSciNet  MATH  Google Scholar 

  20. Bouleau, N., Hirsch, F.: Formes de Dirichlet générales et densité des variables alétoires réelles sur l'espaces de Wiener. J. Funct. Anal. 69, 229–259 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  21. Bourbaki, N.: Topologie générale. Chapitres 5 à 10, Paris: Hermann 1974.

    MATH  Google Scholar 

  22. Cannon, J.T.: Convergence criteria for a sequence of semi groups. Appl. Anal. 5, 23–31 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  23. Carillo-Menendez, S.: Processus de Markov associé à une forme de Dirichlet non symétrique. Z. Wahrsch. verw. Geb. 33, 139–154 (1975). *** DIRECT SUPPORT *** A00I6B21 00009

    Article  MATH  Google Scholar 

  24. Choquet, G.: Lectures on Analysis I: Integration and topological vector spaces. London: Benjamin 1969.

    MATH  Google Scholar 

  25. Choquet, G.: Lectures on Analysis II: Representation Theory. London: Benjamin 1969.

    MATH  Google Scholar 

  26. Dellacherie, C., Meyer, P.A.: Probabilities and potential. Paris: Hermann 1978.

    MATH  Google Scholar 

  27. Deny, J.: Méthodes Hilbertiennes et théorie potentiel. Potential Theory, Centro Internazionale Matematico Estivo, Edizioni Cremonese: Roma 1970.

    MATH  Google Scholar 

  28. Driver, B. K.: A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold, (1991) to appear in J. Funct. Anal.

    Google Scholar 

  29. Driver, B. K.: A Cameron-Martin type quasi-invariance theorem for pinned Brownian motion on a compact Riemannian manifold. UCSD-preprint (1992) to appear in Trans. of A.M.S.

    Google Scholar 

  30. Driver, B., Röckner, M.: Construction of diffusions on path and loop spaces of compact Riemannian manifolds. Preprint (1992). C. R. Acad. Sci., Paris, Série I, in press.

    Google Scholar 

  31. Fukushima, M.: Dirichlet spaces and strong Markov processes. Trans. Amer. Math. Soc. 162, 185–224 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  32. Fukushima, M.: On the generation of Markov processes by symmetric forms. Proceedings 2nd Japan—USSR symposium on probability theory. Lect. Notes in Math. 330, Berlin: Springer 1973.

    Google Scholar 

  33. Fukushima, M.: Dirichlet forms and Markov processes. Amsterdam-Oxford-New York: North Holland (1980).

    MATH  Google Scholar 

  34. Fukushima, M.: On a stochastic calculus related to Dirichlet forms and distorted Brownian motion. Physical Reports 77, 255–262 (1981).

    Article  MathSciNet  Google Scholar 

  35. Fukushima, M.: On absolute continuity of multidimensional symmetrizable diffusions. In: Lecture Notes in Math. 923, 146–176. Berlin-Heidelberg-New York: Springer 1982.

    Google Scholar 

  36. Fukushima, M.: Energy forms and diffusion process. In: Mathematics and Physics, Lectures on recent results. Ed. Streit, L. Singapore: World Scientific Publishing Co. 1984.

    Google Scholar 

  37. Goldstein, J.A.: Semigroups of linear operators and applications. Oxford Math. Monographs. New York: O. U. Press 1985.

    MATH  Google Scholar 

  38. Gross, L.: Abstract Wiener spaces. Proc. 5th Berkeley Symp. Math. Stat. Prob. 2, 31–42 (1965).

    Google Scholar 

  39. Ito, K.: Infinite dimensional Ornstein-Uhlenbeck processes. In: Stochastic Analysis. Ed. K. Ito, 197–224. Amsterdam-Oxford-New York: North Holland 1984.

    Google Scholar 

  40. Kuo, H.: Gaussian measures in Banach spaces. Lect. Notes in Math. 463, 1–224, Berlin-Heidelberg-New York: Springer 1975.

    Google Scholar 

  41. Kusuoka, S.: Dirichlet forms and diffusion processes on Banach spaces. J. Fac. Sci. Univ. Tokyo, Sec. IA 29, 387–400 (1982).

    MathSciNet  MATH  Google Scholar 

  42. LeJan, Y.: Dual Markovian semigroups and processes. In: “Functional Analysis in Markov processes”, 47–75, ed. M. Fukushima. Lect. Notes Math. 923. Berlin: Springer 1982.

    Chapter  Google Scholar 

  43. LeJan, Y.: Quasi-continuous functions and Hunt processes. J. Math. Soc. Japan 35, 37–42 (1983).

    Article  MathSciNet  Google Scholar 

  44. Ma, Z. M., Röckner, M.: An introduction to the theory of (nonsymmetric) Dirichlet forms. Monograph, Springer, to appear September 1992.

    Google Scholar 

  45. Malliavin, P.: Stochastic calculus of variation and hypoelliptic operators. Proc. of the International Symposium on Stochastic Differential Equations Kyoto 1976, Tokyo 1978.

    Google Scholar 

  46. Oshima, Y.: Lectures on Dirichlet forms. Preprint Erlangen (1988).

    Google Scholar 

  47. Reed, M., Simon, B.: Methods of modern mathematical physics I. Functional Analysis. New York-San Francisco-London: Academic Press 1972.

    MATH  Google Scholar 

  48. Reed, M., Simon, B.: Methods of modern mathematical physics II. Fourier Analysis, self-adjointness. New York-San Francisco-London, Academic Press 1975.

    MATH  Google Scholar 

  49. Röckner, M.: Dirichlet forms on infinite dimensional state space and applications. Lectures held at Silivri Summer School. Preprint (1990). To appear.

    Google Scholar 

  50. Röckner, M.: Potential theory on non-locally compact spaces via Dirichlet forms. Preprint (1990). To appear as “main lecture” in: Proceedings “International conference on potential theory, Nagoya 1990”.

    Google Scholar 

  51. Röckner, M., Schmuland, B.: Tightness of general C 1, p -capacities on Banach space. Preprint (1991). To appear in J. Funct. Anal.

    Google Scholar 

  52. Röckner, M., Schmuland, B.: In preparation.

    Google Scholar 

  53. Röckner, M., Wielens, N.: Dirichlet forms—closability and change of speed measure In: “Infinite dimensional analysis and stochastic processes”, Research Notes in Math. 124, 119–144, Editor: S. Albeverio, Boston-London-Melbourne: Pitman 1985.

    Google Scholar 

  54. Röckner, M., Zhang, T.S.: Uniqueness of generalized Schrödinger operators and applications. Preprint (1990). J. Funct. Anal. 105, 187–231 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  55. Schmuland, B.: An alternative compactification for classical Dirichlet forms on topological vector spaces. Stochastics 33 (1990), 75–90.

    MathSciNet  MATH  Google Scholar 

  56. Schwartz, L.: Radon measures on arbitrary topological space and cylindrical measures. London: Oxford University Press 1973.

    MATH  Google Scholar 

  57. Sharpe, M.T.: General theory of Markov processes, New York: Academic Press 1988.

    MATH  Google Scholar 

  58. Silverstein, M.L.: Symmetric Markov Processes. Lecture Notes in Math. 426. Berlin-Heidelberg-New York: Springer 1974.

    MATH  Google Scholar 

  59. Stampacchia, G.: Formes bilinéaires coercitives sur les ensembles convexes. C.R. Acad. Sc., Paris t. 258, Série I, 4413–4416 (1964).

    MathSciNet  MATH  Google Scholar 

  60. Watanabe, S.: Lectures on stochastic differential equations and Malliavin calculus. Berlin-Heidelberg-New York-Tokyo: Springer 1984.

    MATH  Google Scholar 

  61. Wloka, J.: Partielle Differentialgleichungen, Stuttgart: Teubner 1982.

    Book  MATH  Google Scholar 

  62. Yan, J.A.: Generalizations of Gross' and Minlos' theorems. In Séminaire de Probabilités XXII, eds. J. Azema, P.A. Meyer, M. Yor. Lect. Notes in Math. 1372, Springer 1989, 395–404. *** DIRECT SUPPORT *** A00I6B21 00010

    Google Scholar 

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Gianfausto Dell'Antonio Umberto Mosco

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Röckner, M. (1993). General theory of Dirichlet forms and applications. In: Dell'Antonio, G., Mosco, U. (eds) Dirichlet Forms. Lecture Notes in Mathematics, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074093

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  • DOI: https://doi.org/10.1007/BFb0074093

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