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Volumn 42, Issue 3, 2005, Pages 677-722

On the regularity of sample paths of sub-elliptic diffusions on manifolds

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EID: 27944458071     PISSN: 00306126     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (8)

References (58)
  • 1
    • 0033465207 scopus 로고    scopus 로고
    • Brownian motion and harmonic analysis on Sierpinski carpets
    • M. Barlow and R. Bass: Brownian motion and harmonic analysis on Sierpinski carpets, Canad. J. Math. 51 (1999), 673-744.
    • (1999) Canad. J. Math. , vol.51 , pp. 673-744
    • Barlow, M.1    Bass, R.2
  • 2
  • 3
    • 0005348493 scopus 로고    scopus 로고
    • Laws of the iterated logarithm for some symmetric diffusion processes
    • R. Bass and T. Kumagai: Laws of the iterated logarithm for some symmetric diffusion processes, Osaka J. Math. 37 (2000), 625-650.
    • (2000) Osaka J. Math. , vol.37 , pp. 625-650
    • Bass, R.1    Kumagai, T.2
  • 4
    • 0034364413 scopus 로고    scopus 로고
    • On- and off-diagonal heat kernel behaviors on certain infinite dimensional Dirichlet spaces
    • A. Bendikov and L. Saloff-Coste: On- and off-diagonal heat kernel behaviors on certain infinite dimensional Dirichlet spaces, Amer. J. Math. 122 (2000), 1205-1263.
    • (2000) Amer. J. Math. , vol.122 , pp. 1205-1263
    • Bendikov, A.1    Saloff-Coste, L.2
  • 5
    • 0037696886 scopus 로고    scopus 로고
    • On the sample paths of Brownian motions on compact infinite dimensional groups
    • A. Bendikov and L. Saloff-Coste: On the sample paths of Brownian motions on compact infinite dimensional groups, Ann. Probab. 31 (2003), 1464-1493.
    • (2003) Ann. Probab. , vol.31 , pp. 1464-1493
    • Bendikov, A.1    Saloff-Coste, L.2
  • 6
    • 0001340963 scopus 로고
    • Formes de Dirichlet et estimations structurelles dans les milieux discontinus
    • M. Biroli and U. Mosco: Formes de Dirichlet et estimations structurelles dans les milieux discontinus, C.R. Acad. Sci. Paris 313 (1991), 593-598.
    • (1991) C.R. Acad. Sci. Paris , vol.313 , pp. 593-598
    • Biroli, M.1    Mosco, U.2
  • 7
    • 0000067861 scopus 로고
    • A Saint-venant principle for Dirichlet forms on discontinuous media
    • M. Biroli and U. Mosco: A Saint-Venant principle for Dirichlet forms on discontinuous media, Annali Mat. Pura Appl. 169 (1995), 125-181.
    • (1995) Annali Mat. Pura Appl. , vol.169 , pp. 125-181
    • Biroli, M.1    Mosco, U.2
  • 9
    • 0010756407 scopus 로고
    • Opérateurs elliptiques dégénérés associés aux axiomatiques de la théorie du potentiel
    • C.I.M.E. (Stresa, 1969), Rome
    • J.M. Bony: Opérateurs elliptiques dégéné rés associés aux axiomatiques de la théorie du potentiel; in Potential Theory, C.I.M.E. (Stresa, 1969), Rome (1970).
    • (1970) Potential Theory
    • Bony, J.M.1
  • 13
    • 0001563743 scopus 로고    scopus 로고
    • Non-gaussian aspects of heat kernel behaviour
    • E.B. Davies: Non-Gaussian aspects of heat kernel behaviour, J. London Math. Soc. 55 (1997), 105-125.
    • (1997) J. London Math. Soc. , vol.55 , pp. 105-125
    • Davies, E.B.1
  • 15
    • 0001837247 scopus 로고
    • Some problems on random walk in space
    • University of California Press
    • A. Dvoretzky and P. Erdös: Some problems on random walk in space; in Second Berkeley Symp., 1951, 353-367, University of California Press.
    • (1951) Second Berkeley Symp. , pp. 353-367
    • Dvoretzky, A.1    Erdös, P.2
  • 16
    • 0000603332 scopus 로고
    • Fundamental solutions for second order subelliptic operators
    • C. Fefferman and A. Sanchez-Calle: Fundamental solutions for second order subelliptic operators, Annals of Math. 124 (1986), 247-272.
    • (1986) Annals of Math. , vol.124 , pp. 247-272
    • Fefferman, C.1    Sanchez-Calle, A.2
  • 18
    • 27944499310 scopus 로고
    • An integral test for the rate of escape of d-dimensional random walk
    • P. Griffin: An integral test for the rate of escape of d-dimensional random walk, Ann. Probab. 11 (1983), 953-961.
    • (1983) Ann. Probab. , vol.11 , pp. 953-961
    • Griffin, P.1
  • 19
    • 0002209819 scopus 로고
    • The heat equation on non-compact Riemannian manifolds
    • A. Grigor'yan: The heat equation on non-compact Riemannian manifolds, Matem. Sbornik, 182 (1991), 55-87.
    • (1991) Matem. Sbornik , vol.182 , pp. 55-87
    • Grigor'yan, A.1
  • 21
    • 0000083908 scopus 로고    scopus 로고
    • Estimates of the heat kernels on Riemannian manifolds
    • Eds. E.B Davies and Y. Safarov, Cambridge University Press
    • A. Grigor'yan: Estimates of the heat kernels on Riemannian manifolds; in Spectral Theory and Geometry, London Math. Soc. Lecture Note Series 273, Eds. E.B Davies and Y. Safarov, 140-225, Cambridge University Press, 1999.
    • (1999) Spectral Theory and Geometry, London Math. Soc. Lecture Note Series , vol.273 , pp. 140-225
    • Grigor'yan, A.1
  • 22
    • 85065383414 scopus 로고    scopus 로고
    • Escape rate of Brownian motion on Riemannian manifolds
    • A. Grigor'yan: Escape rate of Brownian motion on Riemannian manifolds, Applicable Anal, 71 (1999), 63-89.
    • (1999) Applicable Anal , vol.71 , pp. 63-89
    • Grigor'yan, A.1
  • 23
    • 0039657135 scopus 로고    scopus 로고
    • Analytic and geometric background of recurrence and non-explosion of Brownian motion on Riemannian manifolds
    • A. Grigor'yan: Analytic and geometric background of recurrence and non-explosion of Brownian motion on Riemannian manifolds, Bull. Amer. Math. Soc. 36 (1999), 135-249.
    • (1999) Bull. Amer. Math. Soc. , vol.36 , pp. 135-249
    • Grigor'yan, A.1
  • 24
    • 0036076695 scopus 로고    scopus 로고
    • Hitting probabilities for Brownian motion on Riemannian manifolds
    • A. Grigor'yan and L. Saloff-Coste L: Hitting probabilities for Brownian motion on Riemannian manifolds, J. Math. Pures Appl. 81 (2002), 115-142.
    • (2002) J. Math. Pures Appl. , vol.81 , pp. 115-142
    • Grigor'yan, A.1    Saloff-Coste, L.2
  • 26
    • 84956085473 scopus 로고
    • On a class of hypoelliptic pseudodifferential operators degenerate on a submanifold
    • V. Grushin: On a class of hypoelliptic pseudodifferential operators degenerate on a submanifold, Math. USSR Sbornik 13 (1971), 155-185.
    • (1971) Math. USSR Sbornik , vol.13 , pp. 155-185
    • Grushin, V.1
  • 27
    • 0001926819 scopus 로고
    • Gaussian estimates for Markov chains and random walks on groups
    • W. Hebisch and L. Saloff-Coste: Gaussian estimates for Markov chains and random walks on groups, Ann. Prob. 21 (1993), 673-709.
    • (1993) Ann. Prob. , vol.21 , pp. 673-709
    • Hebisch, W.1    Saloff-Coste, L.2
  • 28
    • 0041034140 scopus 로고    scopus 로고
    • On the relation between elliptic and parabolic Harnack inequalities
    • W. Hebisch and L. Saloff-Coste: On the relation between elliptic and parabolic Harnack inequalities, Ann. Inst. Fourier 51 (2001), 1437-1481.
    • (2001) Ann. Inst. Fourier , vol.51 , pp. 1437-1481
    • Hebisch, W.1    Saloff-Coste, L.2
  • 29
    • 15244346736 scopus 로고
    • Hypoelliptic second order differential equations
    • L. Hörmander: Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147-171.
    • (1967) Acta Math. , vol.119 , pp. 147-171
    • Hörmander, L.1
  • 30
    • 84967773611 scopus 로고
    • Semi-groups of measures on Lie groups
    • G.A. Hunt: Semi-groups of measures on Lie groups, Trans. Amer. Math. Soc. 81 (1956), 264-293.
    • (1956) Trans. Amer. Math. Soc. , vol.81 , pp. 264-293
    • Hunt, G.A.1
  • 32
    • 84972555264 scopus 로고
    • The Poincaré inequality for vector fields satisfying Hörmander condition
    • D. Jerison: The Poincaré inequality for vector fields satisfying Hörmander condition. Duke Math. J. 53 (1986), 503-523.
    • (1986) Duke Math. J. , vol.53 , pp. 503-523
    • Jerison, D.1
  • 33
    • 0001993902 scopus 로고
    • Subelliptic second order differential operators
    • Complex Analysis III
    • D. Jerison and A. Sanchez-Calle: Subelliptic second order differential operators; in Complex Analysis III, Lect. Notes in Math. 1277 (1986), 47-77.
    • (1986) Lect. Notes in Math. , vol.1277 , pp. 47-77
    • Jerison, D.1    Sanchez-Calle, A.2
  • 35
    • 0000324115 scopus 로고
    • On the parabolic kernel of Schrödinger operator
    • P. Li and S-T. Yau: On the parabolic kernel of Schrödinger operator, Acta Math. 156 (1986), 153-201.
    • (1986) Acta Math. , vol.156 , pp. 153-201
    • Li, P.1    Yau, S.-T.2
  • 36
    • 0010276266 scopus 로고
    • Random thoughts on reversible potential theory
    • Summer School in Potential Theory, Joensuu, Ed. Ilpo Laine, University of Joensuu
    • T. Lyons: Random thoughts on reversible potential theory; in Summer School in Potential Theory, Joensuu 1990, Ed. Ilpo Laine, University of Joensuu, Publication in Sciences 26, 71-114.
    • (1990) Publication in Sciences , vol.26 , pp. 71-114
    • Lyons, T.1
  • 37
    • 21844500588 scopus 로고
    • Analyse sur les boules d'un operateur sous-elliptique
    • P. Maheux and L. Saloff-Coste: Analyse sur les boules d'un operateur sous-elliptique, Math. Ann. 303 (1995), 713-740.
    • (1995) Math. Ann. , vol.303 , pp. 713-740
    • Maheux, P.1    Saloff-Coste, L.2
  • 38
    • 84980078895 scopus 로고
    • A Harnack inequality for parabolic differential equations
    • Correction in 20 (1967), 231-236
    • J. Moser: A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 16 (1964), 101-134. Correction in 20 (1967), 231-236.
    • (1964) Comm. Pure Appl. Math. , vol.16 , pp. 101-134
    • Moser, J.1
  • 39
    • 0041862120 scopus 로고
    • Balls and metrics defined by vector fields I: Basic properties
    • A. Nagel, E. Stein and S. Wainger: Balls and metrics defined by vector fields I: basic properties, Acta Math. 55 (1985), 103-147.
    • (1985) Acta Math. , vol.55 , pp. 103-147
    • Nagel, A.1    Stein, E.2    Wainger, S.3
  • 40
    • 0012025726 scopus 로고
    • The rate of escape of random walk
    • W. Pruitt: The rate of escape of random walk, Ann. Probab. 18 (1990), 1417-1461.
    • (1990) Ann. Probab. , vol.18 , pp. 1417-1461
    • Pruitt, W.1
  • 42
    • 84963021360 scopus 로고
    • A note on Poincaré, Sobolev and Harnack inequalities
    • L. Saloff-Coste: A note on Poincaré, Sobolev and Harnack inequalities, Internat. Math. Res. Notices 2 (1992), 27-38.
    • (1992) Internat. Math. Res. Notices , vol.2 , pp. 27-38
    • Saloff-Coste, L.1
  • 43
    • 0001586659 scopus 로고
    • Parabolic Harnack inequality for divergence-form second-order differential operators
    • Potential theory and degenerate partial differential operators (Parma)
    • L. Saloff-Coste: Parabolic Harnack inequality for divergence-form second-order differential operators; In Potential theory and degenerate partial differential operators (Parma). Potential Anal. 4 (1995), 429-467.
    • (1995) Potential Anal. , vol.4 , pp. 429-467
    • Saloff-Coste, L.1
  • 45
    • 84927465241 scopus 로고
    • Some theorems concerning 2-dimensional Brownian motion
    • F. Spitzer: Some theorems concerning 2-dimensional Brownian motion, Trans. Amer. Math. Soc. 87 (1958), 187-197.
    • (1958) Trans. Amer. Math. Soc. , vol.87 , pp. 187-197
    • Spitzer, F.1
  • 47
    • 0001604599 scopus 로고
    • On the geometry defined by Dirichlet forms
    • Seminar on Stochastic Processes, Random Fields and Applications, Ascona, E. Bolthausen et al. Eds. Birkhäuser
    • K-T. Sturm: On the geometry defined by Dirichlet forms; in Seminar on Stochastic Processes, Random Fields and Applications, Ascona, E. Bolthausen et al. Eds. Birkhäuser, Progress in Probability, 36 (1995), 231-242.
    • (1995) Progress in Probability , vol.36 , pp. 231-242
    • Sturm, K.-T.1
  • 49
    • 21844521606 scopus 로고
    • Sharp estimates for capacities and applications to symmetric diffusions
    • K-T. Sturm: Sharp estimates for capacities and applications to symmetric diffusions, Prob. Theory Relat. Fields 103 (1995), 73-89.
    • (1995) Prob. Theory Relat. Fields , vol.103 , pp. 73-89
    • Sturm, K.-T.1
  • 50
    • 84972506714 scopus 로고
    • Analysis on local Dirichlet spaces - II, Upper gaussian estimates for the fundamental solutions of parabolic equations
    • K-T. Sturm: Analysis on local Dirichlet spaces - II, Upper gaussian estimates for the fundamental solutions of parabolic equations, Osaka J. Math. 32 (1995), 275-312.
    • (1995) Osaka J. Math. , vol.32 , pp. 275-312
    • Sturm, K.-T.1
  • 51
    • 0001581975 scopus 로고    scopus 로고
    • Analysis on local Dirichlet spaces - III, The parabolic Harnack inequality
    • K-T. Sturm: Analysis on local Dirichlet spaces - III, The parabolic Harnack inequality, J. Math. Pures Appl. 75 (1996), 273-297.
    • (1996) J. Math. Pures Appl. , vol.75 , pp. 273-297
    • Sturm, K.-T.1
  • 52
    • 0141487473 scopus 로고    scopus 로고
    • The geometric aspect of Dirichlet forms
    • K-T Sturm: The geometric aspect of Dirichlet forms, Studies in Advanced Math. 8 (1998), 233-277.
    • (1998) Studies in Advanced Math. , vol.8 , pp. 233-277
    • Sturm, K.-T.1
  • 53
    • 84972567558 scopus 로고
    • On a martingale method for symmetric diffusion process and its application
    • M. Takeda: On a martingale method for symmetric diffusion process and its application, Osaka J. Math. 26 (1989), 605-623.
    • (1989) Osaka J. Math. , vol.26 , pp. 605-623
    • Takeda, M.1
  • 54
    • 0001420138 scopus 로고
    • Analysis on Lie groups
    • N. Varopoulos: Analysis on Lie groups, J. Funct. Anal. 76 (1988), 346-410.
    • (1988) J. Funct. Anal. , vol.76 , pp. 346-410
    • Varopoulos, N.1
  • 55
    • 0001141252 scopus 로고
    • Small time Gaussian estimates of heat diffusion kernels. Part I: The semigroup technique
    • N. Varopoulos: Small time Gaussian estimates of heat diffusion kernels. Part I: The semigroup technique, Bull. Sci. Math. 113 (1989), 253-277.
    • (1989) Bull. Sci. Math. , vol.113 , pp. 253-277
    • Varopoulos, N.1
  • 56
    • 38249017875 scopus 로고
    • Small time Gaussian estimates of heat diffusion kernels. Part II. The theory of large deviations
    • N. Varopoulos: Small time Gaussian estimates of heat diffusion kernels. Part II. The theory of large deviations, J. Funct. Anal. 93 (1990), 1-33.
    • (1990) J. Funct. Anal. , vol.93 , pp. 1-33
    • Varopoulos, N.1
  • 58
    • 0011182421 scopus 로고    scopus 로고
    • Global heat kernel estimates
    • J. Wang: Global heat kernel estimates, Pacific J. Math. 178 (1997), 377-398.
    • (1997) Pacific J. Math. , vol.178 , pp. 377-398
    • Wang, J.1


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