Theory of capacity on the Wiener space

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


This text consists of four parts.


Banach Lattice Wiener Space Abstract Wiener Space Choquet Capacity Multiparameter Process 
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  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. 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. Markov properties of multiparameter processes and capacities, Probab. Th. Relat. Fields, 103–1 (1995), 45–71Google Scholar
  19. [19]
    F. Hirsch, S. 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

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