Abstract
A short overview is given on foundations and applications of quasi sure analysis
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Airault, Differential calculus on finite codimensional submanifold of the Wiener space, J. Funct. Anal. 100 (1991), 291–316.
H. Airault and P. Malliavin, Intégration géométrique sur l’espace de Wiener, Bull. Sci. Math. 112 (1988), 3–52.
S. Albeverio, M. Fukushima, W. Hansen, Z. Ma, M. Röckner, Invariance result for capacities on the Wiener space, J. Func. Anal. 106 (1992), 35–49.
R. Buckdahn and H. Föllmer, A conditional approach to the anticipating Girsanov transformation, Probab. Theor. Rel. Fields 95 (1993), 311–330.
L. Denis, Analyse quasi-sure de l’approximation d’Euler du flot des EDS, C. R. Acad. Sci., Paris, 1993.
S. Fang, Le calcul différentiel quasi-sure et son application à l’estimation du noyau de la chaleur, Trans. Amer. Math. Soc. 339 (1993), 221–241.
M. Fukushima, Basic properties of the Brownian motion and capacity on the Wiener space, J. Math. Soc. Japan 36 (1984), 171–176.
M. Fukushima and H. Kaneko, On (p, r)-capacities for general Markovian semi-group, in: Inf. Dim. Ana. and Stoch. Proc. (S. Albeverio, ed. ), Pitman, 1985.
E. Getzler, Degree theory for Wiener map, J. Func. Ana. 68 (1986), 388–403.
Z. Huang and J. Ren, Quasi-sure stochastic flow, Stoch. 33 (1990), 149–158.
K. Itô, On Malliavin Tensor Fields, Comm. Pure and Appl. Math 47 (1994), 1–27.
H. Kaneko, On (p,r)-capacities for Markov processes, Osaka J. Math. 23 (1984), 307–319.
T. Kazumi, Refinements in terms of capacities of certain limit theorems on an abstract Wiener space, J. Math. Kyoto Univ. 32 (1992), 1–33.
T. Kazumi and I. Shigekawa, Measures of finite (p, r)-energy and potential on a separable metric space, Sem. Prob. 26, Lecture Notes in Math., vol. 1526, 1992, pp. 415–444.
S. Kusuoka, Analysis on the Wiener space, II, Differential forms, J. Funct. Anal. 103 (1992), 229–274.
M.P. Malliavin and P. Malliavin, Integration on loop groups, I, Quasi invariant measures, J. Funct. Ana. 93 (1990), 207–237.
P. Malliavin, Stochastic calculus of variations and hypoelliptic operators, Int. Symp. on SDE (K. Itô, ed.), Kyoto, 1976, pp. 195–274.
P. Malliavin, Implicit function in finite corank on the Wiener space, Stochastic Analysis (K. Itô, ed.), Katata 1982, North-Holland, 1984, pp. 369–386.
P. Malliavin, Infinite dimensional analysis, Saint Chéron Round Tables, Bull. Sci. Math. (M. Yor, ed.), vol. 117, 1993, pp. 63–90.
P. Malliavin, Universal Wiener Spaces,San Felipe Conference (1993), Birkhäuser, 77–102.
P. Malliavin and D. Nualart, Quasi-sure analysis and Stratanovitch anticipative SDE, Prob. Th. and Rel. Fields 96 (1993), 45–55.
P. Malliavin and D. Nualart, Quasi-sure analysis of stochastic flows, J. Funct. Anal. 112 (1993), 287–317.
Analyse quasi-sure des équations différentielles stochastiques, Bull. Sci. Math. 112 (1990), 187–214.
Topologie p-fine sur l’espace de Wiener et théorie des fonctions implicites,Bull. Sci. Math. 114 (1990), 99–114.
J. Ren, Analyse quasi-sure des martingales régulières, C. R. Acad. Sci. Paris 317 (1993), 299–303.
I. Shigekawa, A quasi homeomorphism of the Wiener space, AMS Summer Institute, Cornell, July, 1993.
H. Sugita, Positive generalized functions and potential theory over an abstract Wiener space, J. Math. Kyoto Univ. 25 (1985), 717–725.
M. Takeda, (p, r)-capacity on the Wieneer space and properties of the Brownian motion, Z. Wahrsch. Verw. Gebiete 68 (1984), 149–162.
J. Van Biesen, The divergence on submanifold of the Wiener space, J. Funct. Ana. 113 (1993), 426–461.
N. Yoshida, A large deviation principle for capacities on the Wiener space, Prob. Th. Rel. Fields 94 (1993), 473–488.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Basel AG
About this paper
Cite this paper
Malliavin, P. (1995). Applications and Foundations of Quasi Sure Analysis. In: Bolthausen, E., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications. Progress in Probability, vol 36. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7026-9_14
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7026-9_14
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7028-3
Online ISBN: 978-3-0348-7026-9
eBook Packages: Springer Book Archive