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Volumn , Issue 2, 2004, Pages 89-108

Weak Poincaré Inequalities on Path Spaces

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EID: 1842632427     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792804130882     Document Type: Article
Times cited : (15)

References (23)
  • 1
    • 0010015342 scopus 로고    scopus 로고
    • Gradient estimates of harmonic functions and the asymptotics of spectral gaps on path spaces
    • S. Aida, Gradient estimates of harmonic functions and the asymptotics of spectral gaps on path spaces, Interdiscip. Inform. Sci. 2 (1996), no. 1, 75-84.
    • (1996) Interdiscip. Inform. Sci. , vol.2 , Issue.1 , pp. 75-84
    • Aida, S.1
  • 2
    • 0035484277 scopus 로고    scopus 로고
    • An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups
    • _, An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups, J. Funct. Anal. 185 (2001), no. 2, 474-526.
    • (2001) J. Funct. Anal. , vol.185 , Issue.2 , pp. 474-526
  • 4
    • 0002414164 scopus 로고
    • Differential calculus on path and loop spaces. I. Logarithmic Sobolev inequalities on path spaces
    • S. Aida and D. Elworthy, Differential calculus on path and loop spaces. I. Logarithmic Sobolev inequalities on path spaces, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 1, 97-102.
    • (1995) C. R. Acad. Sci. Paris Sér. I Math. , vol.321 , Issue.1 , pp. 97-102
    • Aida, S.1    Elworthy, D.2
  • 5
    • 0001550136 scopus 로고
    • Positive harmonic functions on complete manifolds of negative curvature
    • M. T. Anderson and R. Schoen, Positive harmonic functions on complete manifolds of negative curvature, Ann. of Math. (2) 121 (1985), no. 3, 429-461.
    • (1985) Ann. of Math. (2) , vol.121 , Issue.3 , pp. 429-461
    • Anderson, M.T.1    Schoen, R.2
  • 6
    • 0039907778 scopus 로고    scopus 로고
    • Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces
    • M. Capitaine, E. P. Hsu, and M. Ledoux, Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces, Electron. Comm. Probab. 2 (1997), 71-81.
    • (1997) Electron. Comm. Probab. , vol.2 , pp. 71-81
    • Capitaine, M.1    Hsu, E.P.2    Ledoux, M.3
  • 7
    • 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), no. 2, 272-376.
    • (1992) J. Funct. Anal. , vol.110 , Issue.2 , pp. 272-376
    • Driver, B.K.1
  • 8
    • 0000145028 scopus 로고
    • Inégalité du type de Poincaré sur l'espace des chemins riemanniens
    • French
    • S. Fang, Inégalité du type de Poincaré sur l'espace des chemins riemanniens [Poincare-type inequality on a Riemannian path space], C. R. Acad. Sci. Paris Sér. I Math. 318 (1994), no. 3, 257-260 (French).
    • (1994) C. R. Acad. Sci. Paris Sér. I Math. , vol.318 , Issue.3 , pp. 257-260
    • Fang, S.1
  • 9
    • 0001474422 scopus 로고
    • Function Theory on Manifolds Which Possess a Pole
    • Springer-Verlag, Berlin
    • R. E. Greene and H. Wu, Function Theory on Manifolds Which Possess a Pole, Lecture Notes in Mathematics, vol. 699, Springer-Verlag, Berlin, 1979.
    • (1979) Lecture Notes in Mathematics , vol.699
    • Greene, R.E.1    Wu, H.2
  • 10
    • 0010999220 scopus 로고
    • Inégalités de Sobolev logarithmiques sur un espace de chemins
    • French
    • E. P. Hsu, Inégalités de Sobolev logarithmiques sur un espace de chemins {Logarithmic Sobolev inequalities on path spaces], C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 8, 1009-1012 (French).
    • (1995) C. R. Acad. Sci. Paris Sér. I Math. , vol.320 , Issue.8 , pp. 1009-1012
    • Hsu, E.P.1
  • 11
    • 0031487270 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities on path spaces over Riemannian manifolds
    • _, Logarithmic Sobolev inequalities on path spaces over Riemannian manifolds, Comm. Math. Phys. 189 (1997), no. 1, 9-16.
    • (1997) Comm. Math. Phys. , vol.189 , Issue.1 , pp. 9-16
  • 12
    • 0010534606 scopus 로고    scopus 로고
    • Stochastic Analysis on Manifolds
    • American Mathematical Society, Rhode Island
    • _, Stochastic Analysis on Manifolds, Graduate Studies in Mathematics, vol. 38, American Mathematical Society, Rhode Island, 2002.
    • (2002) Graduate Studies in Mathematics , vol.38
  • 13
    • 0000457664 scopus 로고
    • Limiting angle of Brownian motion in certain two-dimensional Cartan-Hadamard manifolds
    • E. P. Hsu and W. S. Kendall, Limiting angle of Brownian motion in certain two-dimensional Cartan-Hadamard manifolds, Ann. Fac. Sci. Toulouse Math. (6) 1 (1992), no. 2, 169-186.
    • (1992) Ann. Fac. Sci. Toulouse Math. (6) , vol.1 , Issue.2 , pp. 169-186
    • Hsu, E.P.1    Kendall, W.S.2
  • 14
    • 0000418027 scopus 로고
    • The radial part of Brownian motion on a manifold: A semimartingale property
    • W. S. Kendall, The radial part of Brownian motion on a manifold: a semimartingale property, Ann. Probab. 15 (1987), no. 4, 1491-1500.
    • (1987) Ann. Probab. , vol.15 , Issue.4 , pp. 1491-1500
    • Kendall, W.S.1
  • 15
    • 0003001404 scopus 로고    scopus 로고
    • Limiting angle of Brownian motion on certain manifolds
    • H. L. Le, Limiting angle of Brownian motion on certain manifolds, Probab. Theory Related Fields 106 (1996), no. 1, 137-149.
    • (1996) Probab. Theory Related Fields , vol.106 , Issue.1 , pp. 137-149
    • Le, H.L.1
  • 16
    • 0035485240 scopus 로고    scopus 로고
    • 2-convergence rates of Markov semigroups
    • 2-convergence rates of Markov semigroups, J. Funct. Anal. 185 (2001), no. 2, 564-603.
    • (2001) J. Funct. Anal. , vol.185 , Issue.2 , pp. 564-603
    • Röckner, M.1    Wang, F.-Y.2
  • 17
    • 84972508386 scopus 로고
    • A lower bound for the first eigenvalue of a negatively curved manifold
    • R. Schoen, A lower bound for the first eigenvalue of a negatively curved manifold, J. Differential Geom. 17 (1982), no. 2, 233-238.
    • (1982) J. Differential Geom. , vol.17 , Issue.2 , pp. 233-238
    • Schoen, R.1
  • 18
    • 0001212955 scopus 로고    scopus 로고
    • Gradient estimates for harmonic functions on regular domains in Riemannian manifolds
    • A. Thalmaier and F.-Y. Wang, Gradient estimates for harmonic functions on regular domains in Riemannian manifolds, J. Funct. Anal. 155 (1998), no. 1, 109-124.
    • (1998) J. Funct. Anal. , vol.155 , Issue.1 , pp. 109-124
    • Thalmaier, A.1    Wang, F.-Y.2
  • 19
    • 0039938081 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities for diffusion processes with application to path space
    • F.-Y. Wang, Logarithmic Sobolev inequalities for diffusion processes with application to path space, Chinese J. Appl. Probab. Statist. 12 (1996), no. 3, 255-264.
    • (1996) Chinese J. Appl. Probab. Statist. , vol.12 , Issue.3 , pp. 255-264
    • Wang, F.-Y.1
  • 20
    • 0041733017 scopus 로고    scopus 로고
    • Spectral gap on path spaces with infinite time-interval
    • _, Spectral gap on path spaces with infinite time-interval, Sci. China Ser. A 42 (1999), no. 6, 600-604.
    • (1999) Sci. China Ser. A , vol.42 , Issue.6 , pp. 600-604
  • 21
    • 0347056958 scopus 로고    scopus 로고
    • Coupling, convergence rates of Markov processes and weak Poincaré inequalities
    • _, Coupling, convergence rates of Markov processes and weak Poincaré inequalities, Sci. China Ser. A 45 (2002), no. 8, 975-983.
    • (2002) Sci. China Ser. A , vol.45 , Issue.8 , pp. 975-983
  • 22
    • 0037209578 scopus 로고    scopus 로고
    • Functional inequalities for the decay of sub-Markov semigroups
    • _, Functional inequalities for the decay of sub-Markov semigroups, Potential Anal. 18 (2003), no. 1, 1-23.
    • (2003) Potential Anal. , vol.18 , Issue.1 , pp. 1-23


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