Smooth probability measures and associated differential operators

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Volumn 2, Issue 1, 1999, Pages 51-78

  Smolyanov, O G ^a   Weizsacker H V ^b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b France   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039666606     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025799000047     Document Type: Article

References (20)

1. H. Airault and P. Malliavin, Intégration géométrique sur l'espace de Wiener, Bull. Sci. Math. 138 (1996) 311-350.
2. V. I. Averbukh, O. G. Smolyanov and S. V. Fomin, Generalized functions and differential equations in linear spaces, I. Differentiate measures, Trudi Moscow Math. Soc. 24 (1971) 133-174.
3. N. Bouleau and F. Hirsch, Dirichlet Forms and Analysis on Wiener Space (Walter de Gruyter, 1991).
4. J. M. Bismut, Martingales, the Malliavin calculus and hypoellipticity under general Hörmander conditions, Z. Wahrsch. Verw. Gebiete 56 (1981) 469-505.
5. Yu. L. Daletskii and S. V. Fomin, Measures and Differential Equations on Infinite Dimensional Spaces (Kluwer, 1992).
6. Yu. L. Daletski and B. D. Maryanin, Smooth measures on infinite dimensional manifolds, Dokl. Akad. Nauk SSSR 285 (1985) 1287-1300.
7. B. Gaveau and P. Trauber, L'intégrale stochastique comme opératuer de divergence dans l'espace fonctionnel, J. Funct. Anal. 46 (1982) 230-238.
8. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis I (Springer, 1979).
9. P. Imkeller and D. Nualart, Integration by parts on Wiener space and the existence of occupation densities, Ann. Prob. 22 (1994) 469-493.
10. A. V. Kirillov, Infinite-dimensional analysis and quantum theory as semimartingale calculus, Russ. Math. Surv. 3 (1994) 41-95.
11. P. Malliavin, Stochastic calculus of variations and hypoelliptic operators, in Proc. of the Int. Conf. on Stochastic Differential Equations (Kinokuniya and Wiley, 1976), pp. 195-263.
12. D. Nualart, The Malliavin Calclulus and Related Topics (Springer, 1995).
13. O. G. Smolyanov, de Rham currents and the Stokes formula in Hilbert spaces, Sov. Math. Dokl. 33 (1986) 140-144.
14. D. Stroock, The Malliavin calculus, a functional analytic approach, J. Funct. Anal. 44 (1981) 212-257.
15. O. G. Smolyanov and H. v. Weizsäcker, Differentiable families of measures, J. Funct. Anal. 118 (1993) 454-476.
16. O. G. Smolyanov and H. v. Weizsäcker, Change of measures and their logarithmic derivatives under smooth transformations, Comp. Ren. Acad. Sci. Paris 321 (1995) 103-108.
17. O. G. Smolyanov and H. v. Weizsäcker, Formulae with logarithmic derivatives of measures related to the quantization of infinite-dimensional Hamiltonian systems, Russ. Mat. Surv. 51 (1996) 357-358.
18. A. V. Uglanov, Surface integrals in a Banach space, Math. USSR Sbor. 38 (1981) 189-217.
19. K. Yosida, Functional Analysis (Springer, 1978), 5th edition.
20. W. P. Ziemer, Weakly Differentiable Functions (Springer, 1989).