Theory of capacity on the Wiener space

  • Francis Hirsch
Part of the Progress in Probability book series (PRPR, volume 38)

Abstract

This text consists of four parts.

Keywords

Stein Librium Rium 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. Bauer Multiparameter processes associated with Ornstein-Uhlenbeck semi-groups, in Classical and Modem Potential Theory and Applications, p. 41–56, Kluwer Acad. Publ., Dortrecht-Boston-London, 1994Google Scholar
  2. [2]
    N. Bouleau, F. Hirsch Dirichlet forms and analysis on Wiener space, Walter de Gruyter, Berlin-New York, 1991Google Scholar
  3. [3]
    L. Denis Analyse quasi-sûre de l’approximation d’Euler et du flot d’une E.D.S., C.R. Acad. Sc. Paris, 315 (1992), 599–602MATHMathSciNetGoogle Scholar
  4. [4]
    L. Denis Convergence quasi-partout pour les capacités définies par un semi- groupe sous-markovien, C.R. Acad. Sc. Paris, 315 (1992), 1033–1036MATHMathSciNetGoogle Scholar
  5. [5]
    L. Denis Analyse quasi-sûre de certaines propriétés classiques sur l’espace de Wiener, Thèse Université Paris V I, 1994Google Scholar
  6. [6]
    D. Feyel Espaces de Banach adaptés. Quasi-topologie et balayage, in Séminaire de théorie du potentiel Paris,No 3. p.81–102, Lecture N. in Math, Vol. 681, Springer-Verlag, Berlin-Heidelberg-New York, 1978Google Scholar
  7. [7]
    D. Feyel, A. de La Pradelle Capacités gaussiennes, A.n. Inst. Fourier, 41-1 (1991), 49–76CrossRefMathSciNetGoogle Scholar
  8. [8]
    D. Feyel, A. de La Pradelle Démonstration géométrique d’une loi du tout ou rien, C.R. A.ad. Sci. Paris, 316 (1993), 229–232MATHMathSciNetGoogle Scholar
  9. [9]
    D. Feyel, A. de La Pradelle On infinite dimensional sheets, Potential Analysis, 4-4 (1995), 345–359CrossRefMathSciNetGoogle Scholar
  10. [10]
    M. Fukushima Basic properties of Brownian motion and a capacity on the Wiener space, J. Math. Soc. Japan, 36-1 (1984), 161–175Google Scholar
  11. [11]
    M. Fukushima A Dirichlet form on the Wiener space and properties of Brownian motion, in Théorie du Potentiel Orsay 1983, p. 290–300, Lecture N. in Math, Vol. 1096, Springer-Ver lag, Berlin-Heidelberg-New York, 1984Google Scholar
  12. [12]
    M. Fukushima Two topics related to Dirichlet forms: quasi everywhere convergences and additive functionals, in CIME courses on Dirichlet forms 1992, p. 21–53, Lecture N. in Math, Vol. 1563, Springer-Ver lag, Berlin-Heidelberg- New York, 1994Google Scholar
  13. [13]
    M. Fukushima, H. Kaneko On (r, p)-capacities for general Markovian semi-groups, in Infinite dimensional analysis and stochastic processes, p. 41–47, Pitman, Boston-London-Melbourne, 1985Google Scholar
  14. [14]
    F. Hirsch Représentation du processus d’Ornstein-Uhlenbeck à n paramètres, in Séminaire de Probabilités XXVII, p. 302–303, Lecture N. in Math, Vol. 1557, Springer-Verlag, Berlin-Heidelberg-New York, 1993Google Scholar
  15. [15]
    F. Hirsch Potential theory related to some multiparameter processes, Potential Analysis, 4-3 (1995), 245–267CrossRefGoogle Scholar
  16. [16]
    F. Hirsch, S. Song Propriétés de Markov des processus à plusieurs paramètres et capacités, C.R. Acad. Sci. Paris, 319 (1994), 483–488MATHMathSciNetGoogle Scholar
  17. [17]
    F. Hirsch, S. Song Inequalities for Bochner’s subordinates of two-parameter symmetric Markov processes, to appear in Ann. I.H.P.Google Scholar
  18. [18]
    F. Hirsch, S. S.ng Markov properties of multiparameter processes and capacities, Probab. Th. Relat. Fields, 103–1 (1995), 45–71Google Scholar
  19. [19]
    F. Hirsch, S. S.ng Symmetric Skorohod topology on n-variable functions and hierarchical Markov properties of n-parameter processes, Probab. Th. Relat. Fields, 103-1 (1995), 25–43Google Scholar
  20. [20]
    Z. Huang, J. Ren Quasi sure stochastic flows, Stochastic and Stoch. Rep., 33 (1990), 149–157Google Scholar
  21. [21]
    T. Kasumi, I. Shigekawa Measures of finite (r,p)-energy and potentials on a separable metric space, in Séminaire de Probabilités XXVI, p. 415–444, Lecture N. in Math, Vol. 1526, Springer-Verlag, Berlin-Heidelberg-New York, 1992Google Scholar
  22. [22]
    N. Kôno 4-dimensional Brownian motion is recurrent with positive capacity, Proc. Japan Acad., 60–21 (1984), 57–59Google Scholar
  23. [23]
    P. Malliavin Implicit functions in finite corank on the Wiener space, in Taniguchi Intern. Symp. on Stochast. Anal Katata 1982, p. 369–386, Kinokuniya, Tokyo, 1983Google Scholar
  24. [24].
    P. Malliavin, D. Nualart Quasi sure analysis of stochastic flows and Banach space valued smooth functionals on the Wiener space, J. Funct. Anal., 112 (1993), 287–317CrossRefMATHMathSciNetGoogle Scholar
  25. [25]
    P.A. Meyer Note sur le processus d’Ornstein-Uhlenbeck, in Séminaire de Probabilités XVI, p. 142–163, Lecture N. in Math, Vol. 511, Springer-Ver lag, Berlin-Heidelberg-New York, 1976Google Scholar
  26. [26]
    J. Ren Topologie P-fine sur l’espace de Wiener et théorème des fonctions implicites, Bull. Sc. math., 114 (1990), 99–114MATHGoogle Scholar
  27. [27]
    J. Ren Analyse quasi-sûre des équations différentielles stochastiques, Bull. Se. math., 114 (1990), 187–213MATHGoogle Scholar
  28. [28]
    I. Shigekawa Sobolev spaces of Banach-valued functions associated with a Markov process, Probab. Th. Relat. Fields, 99 (1994), 425–441CrossRefGoogle Scholar
  29. [29]
    S. Song Inégalités relatives aux processus d’Ornstein-Uhlenbeck à n- paramètres et capacités gaussiennes cn,2, in Séminaire de Probabilités XXVII, p. 276–301, Lecture N. in Math, Vol. 1557, Springer-Verlag, Berlin-Heidelberg- New York, 1993Google Scholar
  30. [30]
    S. Song Construction d’un processus à deux paramètres à partir d’un semigroupe à un paramètre, in Classical and Modem Potential Theory and Applications, p. 419–452, Kluwer Acad. Publ., Dortrecht-Boston-London, 1994Google Scholar
  31. [31]
    E.M. Stein Topics in Harmonie Analysis related to the Littlewood-Paley Theory, Princeton Univ. Press, 1970Google Scholar
  32. [32]
    H. Sugita Positive generalized Wiener functionals and potential theory over abstract Wiener spaces, Osaka J. Math., 25 (1988), 665–696MATHMathSciNetGoogle Scholar
  33. [33]
    J.B. Walsh An introduction to stochastic partial differential equations, in Ecole d’été de probabilités de Saint-Flour XIV-1984, p. 266–437, Lecture N. in Math, Vol. 1180, Springer-Verlag, Berlin-Heidelberg-New York, 1986Google Scholar
  34. [34]
    S. Watanabe On stochastic differential equations and Malliavin calculus, Tata Intitute of Fund. Research, Vol. 73, Springer-Verlag, Berlin-Heidelberg- New York, 1984Google Scholar

Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Francis Hirsch
    • 1
  1. 1.Equipe d’Analyse et ProbabilitésUniversité d’Evry - Val d’EssonneEvry CedexFrance

Personalised recommendations