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Volumn 126, Issue 3, 2003, Pages 395-420

On contraction properties of Markov kernels

Author keywords

Dirichlet form; Dobrushin's ergodic coefficient; Generalized relative entropy; Inhomogeneous Gaussian chains; Lipschitz contraction; Loose of memory property; Markov kernel; Modified logarithmic Sobolev inequality; Orlicz norm; Spectral gap

Indexed keywords


EID: 0043245222     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-003-0270-6     Document Type: Article
Times cited : (54)

References (17)
  • 2
    • 0002432396 scopus 로고    scopus 로고
    • On Sobolev and logarithmic Sobolev inequalities for Markov semigroups
    • K.D. Elworthy, S. Kusuoka, I. Shigekawa, editors. World Scientific
    • Bakry, D.: On Sobolev and logarithmic Sobolev inequalities for Markov semigroups. In: K.D. Elworthy, S. Kusuoka, I. Shigekawa, editors, New Trends in Stochastic Analysis, pp. 43-75. World Scientific, 1997
    • (1997) New Trends in Stochastic Analysis , pp. 43-75
    • Bakry, D.1
  • 3
    • 0001119849 scopus 로고
    • Diffusions hypercontractives
    • Séminaire de probabilités, XIX, 1983/84. Springer, Berlin
    • Bakry, D., Émery, M.: Diffusions hypercontractives. In Séminaire de probabilités, XIX, 1983/84, volume 1123 of Lecture Notes in Math., pp. 177-206. Springer, Berlin, 1985
    • (1985) Lecture Notes in Math. , vol.1123 , pp. 177-206
    • Bakry, D.1    Émery, M.2
  • 5
    • 0001856347 scopus 로고
    • Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten
    • Csiszár, I.: Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten. Magyar Tud. Akad. Mat. Kutató Int. Közl. 8, 85-108 (1963)
    • (1963) Magyar Tud. Akad. Mat. Kutató Int. Közl. , vol.8 , pp. 85-108
    • Csiszár, I.1
  • 6
    • 0002936641 scopus 로고    scopus 로고
    • Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering
    • Springer, Berlin
    • Del Moral, P., et Miclo, L.: Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering. In Séminaire de Probabilités, XXXIV, pp. 1-145. Springer, Berlin, 2000
    • (2000) Séminaire de Probabilités , vol.34 , pp. 1-145
    • Del Moral, P.1    Miclo, L.2
  • 7
    • 15744384461 scopus 로고    scopus 로고
    • preparation, to be published by Springer-Verlag N.Y.
    • Del Moral, P., Miclo, L.: Feynman-Kac formulae. In preparation, to be published by Springer-Verlag N.Y., 2004
    • (2004) Feynman-Kac Formulae
    • Del Moral, P.1    Miclo, L.2
  • 8
    • 0030487036 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities for finite Markov chains
    • Diaconis, P., Saloff-Coste, L.: Logarithmic Sobolev inequalities for finite Markov chains. The Annals of Applied Probability 6(3), 695-750 (1996)
    • (1996) The Annals of Applied Probability , vol.6 , Issue.3 , pp. 695-750
    • Diaconis, P.1    Saloff-Coste, L.2
  • 9
    • 0002434884 scopus 로고
    • Central limit theorem for nonstationary Markov chains, I, II
    • Dobrushin, R.L.: Central limit theorem for nonstationary Markov chains, I, II. Theory of Probability and its Applications. 1(1 and 4), 66-80 and 330-385 (1956)
    • (1956) Theory of Probability and its Applications , vol.1 , Issue.1-4 , pp. 66-80
    • Dobrushin, R.L.1
  • 10
    • 0002590276 scopus 로고
    • Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process
    • Fill, J.A.: Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process. The Annals of Applied Probability 1(1), 62-87 (1991)
    • (1991) The Annals of Applied Probability , vol.1 , Issue.1 , pp. 62-87
    • Fill, J.A.1
  • 12
    • 0009309243 scopus 로고    scopus 로고
    • Remarques sur l'hypercontractivité et l'évolution de l'entropie pour des chaînes de Markov finies
    • J. Azéma, M. Emery, and M. Yor, editors, Séminaire de Probabilités XXXI. Springer-Verlag, Berlin
    • Miclo, L.: Remarques sur l'hypercontractivité et l'évolution de l'entropie pour des chaînes de Markov finies. In: J. Azéma, M. Emery, and M. Yor, editors, Séminaire de Probabilités XXXI, Lecture Notes in Mathematics 1655, pp. 136-167. Springer-Verlag, Berlin, 1997
    • (1997) Lecture Notes in Mathematics , vol.1655 , pp. 136-167
    • Miclo, L.1
  • 13
    • 0041740878 scopus 로고    scopus 로고
    • Notes on the speed of entropic convergence in the central limit theorem
    • Barcelona
    • Miclo, L.: Notes on the speed of entropic convergence in the central limit theorem. Preprint, submitted to the Proceedings of the Conference on Stochastic Inequalities, Barcelona, 2002
    • (2002) Proceedings of the Conference on Stochastic Inequalities
    • Miclo, L.1
  • 15
    • 0000858580 scopus 로고    scopus 로고
    • Lectures on finite Markov chains
    • P. Bernard, editor, Lectures on Probability Theory and Statistics. Ecole d'Eté de Probabilités de Saint-Flour XXVI-1996. Springer-Verlag, Berlin
    • Saloff-Coste, L.: Lectures on finite Markov chains. In P. Bernard, editor, Lectures on Probability Theory and Statistics. Ecole d'Eté de Probabilités de Saint-Flour XXVI-1996, Lecture Notes in Mathematics 1665. Springer-Verlag, Berlin, 1997
    • (1997) Lecture Notes in Mathematics , vol.1665
    • Saloff-Coste, L.1
  • 16
    • 0034367243 scopus 로고    scopus 로고
    • A new modified logarithmic Sobolev inequality for Poisson point processes and several applications
    • Wu, L.: A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probab. Theory Related Fields 118(3), 427-438 (2000)
    • (2000) Probab. Theory Related Fields , vol.118 , Issue.3 , pp. 427-438
    • Wu, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.