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Volumn 128, Issue 2, 2004, Pages 255-321

Essential spectral radius for Markov semigroups (I): Discrete time case

Author keywords

Essential spectral radius; Large deviations; Markov processes

Indexed keywords


EID: 0842346774     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-003-0304-0     Document Type: Article
Times cited : (59)

References (53)
  • 1
    • 51249162906 scopus 로고
    • Optimal Markovian couplings and applications
    • Chen, M.F.: Optimal Markovian couplings and applications. Mathematica Sinica, New Series 10 (3), 260-275 (1994)
    • (1994) Mathematica Sinica, New Series , vol.10 , Issue.3 , pp. 260-275
    • Chen, M.F.1
  • 2
    • 0000699604 scopus 로고    scopus 로고
    • Estimation of spectral gap for Markov chains
    • Chen, M.F.: Estimation of spectral gap for Markov chains. Mathematica Sinica, New Series 12 (4), 337-360 (1996)
    • (1996) Mathematica Sinica, New Series , vol.12 , Issue.4 , pp. 337-360
    • Chen, M.F.1
  • 3
    • 0000490670 scopus 로고    scopus 로고
    • 2-exponential convergence for Markov chains
    • 2-exponential convergence for Markov chains. Stoch. Proc. Appl. 87, 281-297 (2000)
    • (2000) Stoch. Proc. Appl. , vol.87 , pp. 281-297
    • Chen, M.F.1
  • 4
    • 0842272606 scopus 로고
    • Applications of coupling method to estimate of the first eigenvalue on manifolds
    • Chen, M.F., Wang, F.Y.: Applications of coupling method to estimate of the first eigenvalue on manifolds. Science in China Serie A 23 (11), 1130-1140 (1993)
    • (1993) Science in China Serie A , vol.23 , Issue.11 , pp. 1130-1140
    • Chen, M.F.1    Wang, F.Y.2
  • 5
    • 21744453864 scopus 로고    scopus 로고
    • Estimation of spectral gap for elliptic operators
    • Chen, M.F., Wang, F.Y.: Estimation of spectral gap for elliptic operators. Trans. Am. Math. Soc. 349 (3), 1239-1267 (1997)
    • (1997) Trans. Am. Math. Soc. , vol.349 , Issue.3 , pp. 1239-1267
    • Chen, M.F.1    Wang, F.Y.2
  • 7
    • 0003794206 scopus 로고
    • Schrödinger operators with Application to Quantum Mechanics and Global Goemetry
    • Springer-Verlag
    • Cyon, H.L., Froese, R.G., Kirsch, W., Simon, B.: Schrödinger operators with Application to Quantum Mechanics and Global Goemetry. Text and Monographs in Physics, Springer-Verlag, 1987
    • (1987) Text and Monographs in Physics
    • Cyon, H.L.1    Froese, R.G.2    Kirsch, W.3    Simon, B.4
  • 8
    • 0040108304 scopus 로고
    • Upper bounds for large deviations of dependent random vectors
    • de Acosta, A.: Upper bounds for large deviations of dependent random vectors. Z. Wahrsch. verw. Geb. 69, 551-565 (1985)
    • (1985) Z. Wahrsch. Verw. Geb. , vol.69 , pp. 551-565
    • De Acosta, A.1
  • 9
    • 0000331489 scopus 로고
    • Large deviations for vector valued additive functionals of a Markov process: Lower bound
    • de Acosta, A.: Large deviations for vector valued additive functionals of a Markov process: lower bound. Ann. Probab. 16, 925-960 (1988)
    • (1988) Ann. Probab. , vol.16 , pp. 925-960
    • De Acosta, A.1
  • 12
    • 0011509406 scopus 로고
    • Measures of non-compactness of operators in Banach lattices
    • de Pagter, B., Schep, A.R.: Measures of non-compactness of operators in Banach lattices. J. Funct. Anal. 78, 31-55 (1988)
    • (1988) J. Funct. Anal. , vol.78 , pp. 31-55
    • De Pagter, B.1    Schep, A.R.2
  • 14
    • 0013296475 scopus 로고    scopus 로고
    • Sur les propriétés asymptotiques du mouvement régis par certain types de chaîne simples
    • Doeblin, W.: Sur les propriétés asymptotiques du mouvement régis par certain types de chaîne simples. Bull. Math. Soc. Roum. Sci. 39 (1), 57-115; (2), 3-61 (1937)
    • Bull. Math. Soc. Roum. Sci. , vol.39 , Issue.1 , pp. 57-115
    • Doeblin, W.1
  • 15
    • 0842337260 scopus 로고
    • Doeblin, W.: Sur les propriétés asymptotiques du mouvement régis par certain types de chaîne simples. Bull. Math. Soc. Roum. Sci. 39 (1), 57-115; (2), 3-61 (1937)
    • (1937) Bull. Math. Soc. Roum. Sci. , Issue.2 , pp. 3-61
  • 16
    • 0009184411 scopus 로고
    • Eléments d'une théorie générale des chaines simples constantes de Markov
    • Doeblin, W.: Eléments d'une théorie générale des chaines simples constantes de Markov. Ann. Sci. de l'Ecole Normale Sup. 57 (III), 61-111 (1940)
    • (1940) Ann. Sci. de l'Ecole Normale Sup. , vol.57 , Issue.3 , pp. 61-111
    • Doeblin, W.1
  • 17
    • 84980178612 scopus 로고
    • Asymptotic evaluation of certain Markov process expectations for large time, I-IV
    • Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time, I-IV. Comm. Pur. Appl. Math. 28, 1-47 and 279-301 (1975); 29, 389-461 (1976); 36, 183-212 (1983)
    • (1975) Comm. Pur. Appl. Math. , vol.28 , pp. 1-47
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 18
    • 84980151353 scopus 로고
    • Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time, I-IV. Comm. Pur. Appl. Math. 28, 1-47 and 279-301 (1975); 29, 389-461 (1976); 36, 183-212 (1983)
    • (1976) Comm. Pur. Appl. Math. , vol.29 , pp. 389-461
  • 19
    • 84990587390 scopus 로고
    • Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time, I-IV. Comm. Pur. Appl. Math. 28, 1-47 and 279-301 (1975); 29, 389-461 (1976); 36, 183-212 (1983)
    • (1983) Comm. Pur. Appl. Math. , vol.36 , pp. 183-212
  • 22
    • 22044456340 scopus 로고    scopus 로고
    • On Persson's theorem in local Dirichlet spaces
    • Grillo, G.: On Persson's theorem in local Dirichlet spaces. Z. Anal. Anwendungen 17 (2), 329-338 (1998)
    • (1998) Z. Anal. Anwendungen , vol.17 , Issue.2 , pp. 329-338
    • Grillo, G.1
  • 23
    • 0001309666 scopus 로고
    • ∞. Z.W. 24, 263-274 (1972)
    • (1972) Z.W. , vol.24 , pp. 263-274
    • Horowitz, S.1
  • 24
    • 0038992289 scopus 로고
    • Large deviations for additive functionals of Markov processes
    • Jain, N.C.: Large deviations for additive functionals of Markov processes. Ann. Probab. 17 (3), 1073-1098 (1990)
    • (1990) Ann. Probab. , vol.17 , Issue.3 , pp. 1073-1098
    • Jain, N.C.1
  • 26
    • 0038245923 scopus 로고
    • Denumerable Markov chains
    • Springer-Verlag
    • Kemeny, J.G., Snell, J.L., Knapp, A.W.: Denumerable Markov chains. GTM 40, Springer-Verlag, 1976
    • (1976) GTM , vol.40
    • Kemeny, J.G.1    Snell, J.L.2    Knapp, A.W.3
  • 27
    • 0001967887 scopus 로고
    • Unitary dilations of Markov transition operators and the corresponding integral representation for transition probability matrices
    • U. Grenander, (ed.), Almqvist and Wiksell, Stockholm
    • Kendall, D.G.: Unitary dilations of Markov transition operators and the corresponding integral representation for transition probability matrices. In: Probability and Statistics, U. Grenander, (ed.), Almqvist and Wiksell, Stockholm, 1959, pp. 139-161
    • (1959) Probability and Statistics , pp. 139-161
    • Kendall, D.G.1
  • 28
    • 0000458262 scopus 로고    scopus 로고
    • Concentration of measure and logarithmic Sobolev inequalities
    • Séminaire de Probab. XXXIII, Springer
    • Ledoux, M.: Concentration of measure and logarithmic Sobolev inequalities. Séminaire de Probab. XXXIII, LNM 1709, 120-216, Springer, (1999)
    • (1999) LNM , vol.1709 , pp. 120-216
    • Ledoux, M.1
  • 30
    • 0642306596 scopus 로고
    • 2 convergence of attractive reversible nearest particle systems
    • 2 convergence of attractive reversible nearest particle systems. Ann. Probab. 17 (2), 403-432 (1989)
    • (1989) Ann. Probab. , vol.17 , Issue.2 , pp. 403-432
    • Ligget, T.M.1
  • 32
    • 0002261059 scopus 로고
    • Ergodicity, continuity and analyticity of countable Markov chains
    • Malyshev, V.A., Men'sikov, M.V.: Ergodicity, continuity and analyticity of countable Markov chains. Trans. Moscow Math. Soc. 1 1-48 (1982)
    • (1982) Trans. Moscow Math. Soc. , vol.1 , pp. 1-48
    • Malyshev, V.A.1    Men'sikov, M.V.2
  • 35
    • 0033173868 scopus 로고    scopus 로고
    • Relation entre isopérimétrie et trou spectral pour les chaî nes de Markov finies
    • Miclo, L.: Relation entre isopérimétrie et trou spectral pour les chaî nes de Markov finies. Probab. Th. Rel. Fields 114, 431-485 (1999)
    • (1999) Probab. Th. Rel. Fields , vol.114 , pp. 431-485
    • Miclo, L.1
  • 36
    • 0003207468 scopus 로고
    • One-Parameter Semigroups of Positive Operators
    • Springer-Verlag, Berlin
    • Nagel, R.: One-Parameter Semigroups of Positive Operators. Lect. Notes in Math. 1184, Springer-Verlag, Berlin, 1986
    • (1986) Lect. Notes in Math. , vol.1184
    • Nagel, R.1
  • 37
    • 0003209629 scopus 로고
    • General Irreducible Markov Chains and Non-Negative operators
    • Cambridge University Press
    • Nummelin, E.: General Irreducible Markov Chains and Non-Negative operators. Cambridge Tracts in Math., 83, Cambridge University Press, 1984
    • (1984) Cambridge Tracts in Math. , vol.83
    • Nummelin, E.1
  • 38
    • 0000099991 scopus 로고
    • Geometric ergodicity of Harris recurrent Markov chains with applications to renewel theory
    • Nummelin, E., Tuominen, P.: Geometric ergodicity of Harris recurrent Markov chains with applications to renewel theory. Stoch. Proc. Appl. 12, 187-202 (1982)
    • (1982) Stoch. Proc. Appl. , vol.12 , pp. 187-202
    • Nummelin, E.1    Tuominen, P.2
  • 39
    • 0010862224 scopus 로고
    • The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewel theory
    • Nummelin, E., Tuominen, P.: The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewel theory. Stoch. Proc. Appl. 15, 295-311 (1983)
    • (1983) Stoch. Proc. Appl. , vol.15 , pp. 295-311
    • Nummelin, E.1    Tuominen, P.2
  • 40
    • 84972570025 scopus 로고
    • The radius of the essential spectrum
    • Nussbaum, R.D.: The radius of the essential spectrum. Duke Math. J. 38, 473-478 (1970)
    • (1970) Duke Math. J. , vol.38 , pp. 473-478
    • Nussbaum, R.D.1
  • 44
    • 0000593993 scopus 로고    scopus 로고
    • Functional inequalities for empty essential spectrum
    • Wang, F.Y.: Functional inequalities for empty essential spectrum. J. Funct. Anal. 170, 219-245 (2000)
    • (2000) J. Funct. Anal. , vol.170 , pp. 219-245
    • Wang, F.Y.1
  • 47
    • 0001415423 scopus 로고
    • Moderate deviations of dependent random variables related to CLT
    • Wu, L.M.: Moderate deviations of dependent random variables related to CLT, Ann. Probab. 23, 420-445 (1995)
    • (1995) Ann. Probab. , vol.23 , pp. 420-445
    • Wu, L.M.1
  • 48
    • 0042385367 scopus 로고    scopus 로고
    • An introduction to large deviations (in chinese)
    • J.A. Yan, S. Peng, S. Fang, L. Wu, (eds.), Press of Sciences of China, Beijing
    • Wu, L.M.: An introduction to large deviations (in chinese). In: Several Topics in Stochastic Analysis J.A. Yan, S. Peng, S. Fang, L. Wu, (eds.), Press of Sciences of China, Beijing, pp. 225-336
    • Several Topics in Stochastic Analysis , pp. 225-336
    • Wu, L.M.1
  • 49
    • 0000038655 scopus 로고    scopus 로고
    • Uniformly integrable operators and large deviations for Markov processes
    • Wu, L.M.: Uniformly integrable operators and large deviations for Markov processes. J. Funct. Anal. 172, 301-376 (2000)
    • (2000) J. Funct. Anal. , vol.172 , pp. 301-376
    • Wu, L.M.1
  • 50
    • 0346679040 scopus 로고    scopus 로고
    • Some notes on large deviations of Markov processes
    • Wu, L.M.: Some notes on large deviations of Markov processes. Acta Math. Sinica. English Series 16, 369-394 (2000)
    • (2000) Acta Math. Sinica. English Series , vol.16 , pp. 369-394
    • Wu, L.M.1
  • 51
    • 0012871505 scopus 로고    scopus 로고
    • Large and moderate deviations and exponential convergence for stochastic damping Hamilton systems
    • Wu, L.M.: Large and moderate deviations and exponential convergence for stochastic damping Hamilton systems. Stoch. Proc. Appl. 91 (2), 205-238 (2001)
    • (2001) Stoch. Proc. Appl. , vol.91 , Issue.2 , pp. 205-238
    • Wu, L.M.1


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