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Volumn 39, Issue 2, 1999, Pages 179-210

The Lie Bracket of Adapted Vector Fields on Wiener Spaces

Author keywords

Integration by parts; It development map; Lie bracket; Wiener measure

Indexed keywords

INTEGRATION; MATHEMATICAL OPERATORS;

EID: 0033102265     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900103     Document Type: Article
Times cited : (17)

References (45)
  • 1
    • 0039493410 scopus 로고
    • On the essential selfadjointness of Dirichlet operators on group-valued path space
    • E. Acosta, On the essential selfadjointness of Dirichlet operators on group-valued path space, Proc. Amer. Math. Soc. 122(2) (1994), 581-590.
    • (1994) Proc. Amer. Math. Soc. , vol.122 , Issue.2 , pp. 581-590
    • Acosta, E.1
  • 3
    • 0000116008 scopus 로고
    • Sobolev spaces over loop groups
    • S. Aida, Sobolev spaces over loop groups, J. Funct. Anal. 127(1) (1995), 155-172.
    • (1995) J. Funct. Anal. , vol.127 , Issue.1 , pp. 155-172
    • Aida, S.1
  • 4
    • 0011045450 scopus 로고    scopus 로고
    • On the irreducibility of certain Dirichlet forms on loop spaces over compact homogeneous spaces
    • New Trends in Stochastic Analysis (New Jersey) (K. D. Elworthy, S. Kusuoka, and I. Shigekawa, eds.), World Scientific, Singapore
    • S. Aida, On the irreducibility of certain Dirichlet forms on loop spaces over compact homogeneous spaces, in New Trends in Stochastic Analysis (New Jersey) (K. D. Elworthy, S. Kusuoka, and I. Shigekawa, eds.), Proceedings of the 1994 Taniguchi Symposium, World Scientific, Singapore, 1997, pp. 3-42.
    • (1997) Proceedings of the 1994 Taniguchi Symposium , pp. 3-42
    • Aida, S.1
  • 5
    • 0002414164 scopus 로고
    • Differential calculus on path and loop spaces, I. Logarithmic Sobolev inequalities on path and loop spaces
    • S. Aida and D. Elworthy, Differential calculus on path and loop spaces, I. Logarithmic Sobolev inequalities on path and loop spaces, C. R. Acad. Sci. Paris Sér. I. Math. 321 (1995), 97-102.
    • (1995) C. R. Acad. Sci. Paris Sér. I. Math. , vol.321 , pp. 97-102
    • Aida, S.1    Elworthy, D.2
  • 6
    • 0002041783 scopus 로고
    • Integration on loop group, H, Heat equation for the Wiener measure
    • H. Airault and P. Malliavin, Integration on loop group, H, Heat equation for the Wiener measure, J. Funct. Anal. 104 (1992), 71-109.
    • (1992) J. Funct. Anal. , vol.104 , pp. 71-109
    • Airault, H.1    Malliavin, P.2
  • 8
  • 11
    • 0000161212 scopus 로고
    • 2 pour des intégrales stochastiques anticipatives sur une variété riemannienne
    • 2 pour des intégrales stochastiques anticipatives sur une variété riemannienne, C. R. Acad. Sci. Paris Sér. I Math. 321(9) (1995), 1245-1250.
    • (1995) C. R. Acad. Sci. Paris Sér. I Math. , vol.321 , Issue.9 , pp. 1245-1250
    • Cruzeiro, A.-B.1    Fang, S.2
  • 12
    • 0001616699 scopus 로고
    • Repre mobile et geometrie Riemannienne sur les espaces de chemins
    • A.-B. Cruzeiro and P. Malliavin, Repre mobile et geometrie Riemannienne sur les espaces de chemins, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), 856-864.
    • (1994) C. R. Acad. Sci. Paris Sér. I Math. , vol.319 , pp. 856-864
    • Cruzeiro, A.-B.1    Malliavin, P.2
  • 13
    • 0000901997 scopus 로고
    • Courbures de l'espace de Probabilité d'un brownien Riemannien
    • A.-B. Cruzeiro and P. Malliavin, Courbures de l'espace de Probabilité d'un brownien Riemannien, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), 603-607.
    • (1995) C. R. Acad. Sci. Paris Sér. I Math. , vol.320 , pp. 603-607
    • Cruzeiro, A.-B.1    Malliavin, P.2
  • 14
    • 0030578297 scopus 로고    scopus 로고
    • Renormalization differential geometry on path space: Structural equation, curvature
    • A.-B. Cruzeiro and P. Malliavin, Renormalization differential geometry on path space: structural equation, curvature, J. Funct. Anal. 139 (1996), 119-181.
    • (1996) J. Funct. Anal. , vol.139 , pp. 119-181
    • Cruzeiro, A.-B.1    Malliavin, P.2
  • 15
    • 44049121803 scopus 로고
    • A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
    • B. K. Driver, A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold, J. Funct. Anal. 110 (1992), 272-376.
    • (1992) J. Funct. Anal. , vol.110 , pp. 272-376
    • Driver, B.K.1
  • 16
    • 0542412598 scopus 로고
    • A Cameron-Martin type quasi-invariance theorem for pinned Brownian motion on a compact Riemannian manifold
    • B. K. Driver, A Cameron-Martin type quasi-invariance theorem for pinned Brownian motion on a compact Riemannian manifold, Trans. Amer. Math. Soc. 342 (1994), 375-395.
    • (1994) Trans. Amer. Math. Soc. , vol.342 , pp. 375-395
    • Driver, B.K.1
  • 17
    • 0347590083 scopus 로고
    • The non-equivalence of Dirichlet forms on path spaces
    • Stochastic Analysis on Infinite Dimensional Spaces (H. Kunita, and H.-H. Kuo, eds.), Longman, Essex
    • B. K. Driver, The non-equivalence of Dirichlet forms on path spaces, in Stochastic Analysis on Infinite Dimensional Spaces (H. Kunita, and H.-H. Kuo, eds.), Pitman Research Notes in Mathematics Series, Vol. 310, Longman, Essex, 1994 pp. 75-88.
    • (1994) Pitman Research Notes in Mathematics Series , vol.310 , pp. 75-88
    • Driver, B.K.1
  • 18
    • 0001012278 scopus 로고
    • Towards calculus and geometry on path spaces
    • Stochastic Analysis, Summer Research Institute on Stochastic Analysis, July 11-30, Cornell University (M. Cranston and M. Pinsky, eds.), American Mathematical Society, RI
    • B. K. Driver, Towards calculus and geometry on path spaces, in Stochastic Analysis, Summer Research Institute on Stochastic Analysis, July 11-30, 1993, Cornell University (M. Cranston and M. Pinsky, eds.), Proceedings of Symposia in Pure Mathematics, Vol. 57, American Mathematical Society, RI, 1995, pp. 405-422.
    • (1993) Proceedings of Symposia in Pure Mathematics , vol.57 , pp. 405-422
    • Driver, B.K.1
  • 20
    • 0001010672 scopus 로고
    • Construction of diffusions on path and loop spaces of compact Riemannian manifolds
    • B. K. Driver and M. Röckner, Construction of diffusions on path and loop spaces of compact Riemannian manifolds, C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), 603-608.
    • (1992) C. R. Acad. Sci. Paris Sér. I Math. , vol.315 , pp. 603-608
    • Driver, B.K.1    Röckner, M.2
  • 21
    • 0000031706 scopus 로고
    • Formulae for the derivatives of heat semigroups
    • K. D. Elworthy and X.-M. Li, Formulae for the derivatives of heat semigroups, J. Funct. Anal. 125 (1994), 252-286.
    • (1994) J. Funct. Anal. , vol.125 , pp. 252-286
    • Elworthy, K.D.1    Li, X.-M.2
  • 22
    • 0002621570 scopus 로고    scopus 로고
    • A class of integration by parts formulae in stochastic analysis, I
    • Springer-Verlag, Tokyo
    • K. D. Elworthy and X.-M. Li, A class of integration by parts formulae in stochastic analysis, I, in Itô's Stochastic Calculus and Probability Theory, Springer-Verlag, Tokyo, 1996, pp. 15-30.
    • (1996) Itô's Stochastic Calculus and Probability Theory , pp. 15-30
    • Elworthy, K.D.1    Li, X.-M.2
  • 24
    • 58149364652 scopus 로고
    • Towards a Riemannian geometry on the path space over a Riemannian manifold
    • O. Enchev and D. W. Stroock, Towards a Riemannian geometry on the path space over a Riemannian manifold. J. Funct. Anal. 134(2) (1995), 392-416.
    • (1995) J. Funct. Anal. , vol.134 , Issue.2 , pp. 392-416
    • Enchev, O.1    Stroock, D.W.2
  • 25
    • 0001056103 scopus 로고
    • Integration by parts for pinned Brownian motion
    • O. Enchev and D. W. Stroock, Integration by parts for pinned Brownian motion, Math. Res. Lett. 2, (1995) 161-169.
    • (1995) Math. Res. Lett. , vol.2 , pp. 161-169
    • Enchev, O.1    Stroock, D.W.2
  • 26
    • 84972555817 scopus 로고
    • Brownian motion on the path space of a compact Lie group
    • J. B. Epperson and T. Lohrenz, Brownian motion on the path space of a compact Lie group, Pacific J. Math. 161 (1993), 233-253.
    • (1993) Pacific J. Math. , vol.161 , pp. 233-253
    • Epperson, J.B.1    Lohrenz, T.2
  • 27
    • 0346958914 scopus 로고
    • Diffusions on finite-energy loop spaces
    • J. B. Epperson and T. Lohrenz, Diffusions on finite-energy loop spaces, Soochow J. Math. 20(1) (1994), 113-136.
    • (1994) Soochow J. Math. , vol.20 , Issue.1 , pp. 113-136
    • Epperson, J.B.1    Lohrenz, T.2
  • 29
    • 0001266098 scopus 로고
    • Stochastic anticipative integrals on a Riemannian manifold
    • S. Fang, Stochastic anticipative integrals on a Riemannian manifold, J. Funct. Anal. 131(1) (1995), 228-253.
    • (1995) J. Funct. Anal. , vol.131 , Issue.1 , pp. 228-253
    • Fang, S.1
  • 30
    • 0001365301 scopus 로고
    • Platitude de la structure riemannienne sur le groupe des chemins et identit d'nergie pour les intégrales stochastiques
    • S. Fang and J. Franchi, Platitude de la structure riemannienne sur le groupe des chemins et identit d'nergie pour les intégrales stochastiques, C. R. Acad. Sci. Paris Sér. I Math. 321(10) (1995), 1371-1376.
    • (1995) C. R. Acad. Sci. Paris Sér. I Math. , vol.321 , Issue.10 , pp. 1371-1376
    • Fang, S.1    Franchi, J.2
  • 31
    • 38248998522 scopus 로고
    • Stochastic analysis on the path space of a Riemannian manifold
    • S. Fang and P. Malliavin, Stochastic analysis on the path space of a Riemannian manifold, J. Funct. Anal. 118 (1993), 249-274.
    • (1993) J. Funct. Anal. , vol.118 , pp. 249-274
    • Fang, S.1    Malliavin, P.2
  • 32
    • 0001625329 scopus 로고
    • Logarithmic Soholev inequalities on loop groups
    • L. Gross, Logarithmic Soholev inequalities on loop groups, J. Funct. Anal. 102, (1992), 268-313.
    • (1992) J. Funct. Anal. , vol.102 , pp. 268-313
    • Gross, L.1
  • 33
    • 0001572330 scopus 로고
    • Uniqueness of ground states for Schrodinger operators over loop groups
    • L. Gross, Uniqueness of ground states for Schrodinger operators over loop groups, J. Funct. Anal. 112 (1993), 373-441.
    • (1993) J. Funct. Anal. , vol.112 , pp. 373-441
    • Gross, L.1
  • 34
    • 0001668970 scopus 로고
    • Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold
    • E. P. Hsu, Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold. J. Funct. Anal. 134(2) (1995), 417-450.
    • (1995) J. Funct. Anal. , vol.134 , Issue.2 , pp. 417-450
    • Hsu, E.P.1
  • 35
    • 0010985772 scopus 로고
    • Flows and quasi-invariance of the Wiener measure on path spaces
    • Stochastic Analysis, Summer Research Institute on Stochastic Analysis, July 11-30, Cornell University (M. Cranstar and M. Pinsky, eds.), American Mathematical Society, Providence, RI
    • E. P. Hsu, Flows and quasi-invariance of the Wiener measure on path spaces, in Stochastic Analysis, Summer Research Institute on Stochastic Analysis, July 11-30, 1993, Cornell University (M. Cranstar and M. Pinsky, eds.), Proceedings of Symposia in Pure Mathematics, vol. 57, American Mathematical Society, Providence, RI, 1995, pp. 265-279.
    • (1993) Proceedings of Symposia in Pure Mathematics , vol.57 , pp. 265-279
    • Hsu, E.P.1
  • 36
    • 0010999220 scopus 로고
    • Inégalités de Sobolev logarithmiques sur un espace de chemins
    • E. P. Hsu, Inégalités de Sobolev logarithmiques sur un espace de chemins, C. R. Acad. Sci. Paris Sér. I Math. 320(8) (1995), 1009-1012.
    • (1995) C. R. Acad. Sci. Paris Sér. I Math. , vol.320 , Issue.8 , pp. 1009-1012
    • Hsu, E.P.1
  • 38
    • 0000438918 scopus 로고
    • p Chen forms on loop spaces
    • (M. Barlow and N. Bringham, eds.), Cambridge University Press, Cambridge
    • p Chen forms on loop spaces, in Stochastic Analysis (M. Barlow and N. Bringham, eds.), Cambridge University Press, Cambridge, 1991, pp. 104-162.
    • (1991) Stochastic Analysis , pp. 104-162
    • Jones, J.D.S.1    Leandre, R.2
  • 40
    • 0000252704 scopus 로고
    • Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces
    • R. Leandre, Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces, J. Geom. Phys. 11 (1993), 517-528.
    • (1993) J. Geom. Phys. , vol.11 , pp. 517-528
    • Leandre, R.1
  • 42
    • 0000071236 scopus 로고
    • Integration on loop groups. I. Quasi-invariant measures, quasi-invariant integration on loop groups
    • M.-P. Malliavin and P. Malliavin, Integration on loop groups. I. Quasi-invariant measures, quasi-invariant integration on loop groups, J. Funct. Anal. 93 (1990), 207-237.
    • (1990) J. Funct. Anal. , vol.93 , pp. 207-237
    • Malliavin, M.-P.1    Malliavin, P.2
  • 43
    • 0001918078 scopus 로고
    • Integration on loop group. III; Asymptotic Peter-Weyl orthogonality
    • M.-P. Malliavin and P. Malliavin, Integration on loop group. III; Asymptotic Peter-Weyl orthogonality, J. Funct. Anal. 108 (1992), 13-46.
    • (1992) J. Funct. Anal. , vol.108 , pp. 13-46
    • Malliavin, M.-P.1    Malliavin, P.2
  • 44
    • 58149364016 scopus 로고
    • Twisted sheets
    • J. R. Norris, Twisted sheets, J. Funct. Anal. 132 (1995), 273-334.
    • (1995) J. Funct. Anal. , vol.132 , pp. 273-334
    • Norris, J.R.1


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