메뉴 건너뛰기




Volumn 116, Issue 1, 2000, Pages 89-123

On the limit laws of the second order for additive functionals of Harris recurrent Markov chains

Author keywords

Harris recurrence; Law of the iterated logarithm; Regularity; Weak convergence

Indexed keywords


EID: 0034405097     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00008724     Document Type: Article
Times cited : (15)

References (31)
  • 1
    • 0000331489 scopus 로고
    • Large deviations for vector-valued functional of a Markov chain: Lower bounds
    • de Acosta, A., Large deviations for vector-valued functional of a Markov chain: lower bounds. Ann. Probab. 16, 925-960 (1988)
    • (1988) Ann. Probab. , vol.16 , pp. 925-960
    • De Acosta, A.1
  • 2
    • 0042878084 scopus 로고    scopus 로고
    • Moderate deviations for empirical measures of Markov chains: Upper bounds
    • de Acosta and Chen, X., Moderate deviations for empirical measures of Markov chains: upper bounds. J. Theor. Probab. 11, 1075-1110 (1998)
    • (1998) J. Theor. Probab. , vol.11 , pp. 1075-1110
    • De Acosta1    Chen, X.2
  • 3
    • 0000991156 scopus 로고
    • A new approach to the limit theory of recurrent Markov chains
    • Athreya, K. B. and Ney, P., A new approach to the limit theory of recurrent Markov chains. Trans. Amer. Math. Soc. 245, 493-501 (1988)
    • (1988) Trans. Amer. Math. Soc. , vol.245 , pp. 493-501
    • Athreya, K.B.1    Ney, P.2
  • 4
    • 0032623106 scopus 로고    scopus 로고
    • Limit theorems for functionals of ergodic Markov chains in general state space
    • Chen, X., Limit Theorems for Functionals of Ergodic Markov Chains in General State Space. Memoirs of the AMS. 139, No. 664 (1999)
    • (1999) Memoirs of the AMS , vol.139 , Issue.664
    • Chen, X.1
  • 5
    • 0042136991 scopus 로고    scopus 로고
    • The law of the iterated logarithm for functionals of Harris recurrent Markov chains: Self normalization
    • Chen, X., The law of the iterated logarithm for functionals of Harris recurrent Markov chains: self normalization. J. Theor. Probab. 12, 421-445 (1999)
    • (1999) J. Theor. Probab. , vol.12 , pp. 421-445
    • Chen, X.1
  • 6
    • 85037762891 scopus 로고    scopus 로고
    • How often does a Harris recurrent Markov chain recur?
    • to appear
    • Chen, X., How often does a Harris recurrent Markov chain recur? Ann. Probab. (to appear).
    • Ann. Probab.
    • Chen, X.1
  • 8
    • 0000168954 scopus 로고
    • On additive functionals of Markov chains
    • Csáki, E. and Csörgö, M., On additive functionals of Markov chains. J. Theor. Probab. 8, 905-919 (1995)
    • (1995) J. Theor. Probab. , vol.8 , pp. 905-919
    • Csáki, E.1    Csörgö, M.2
  • 9
    • 0002227667 scopus 로고    scopus 로고
    • On the additive functionals of diffusion processes
    • Csáki, E. and Salminen, P., On the additive functionals of diffusion processes. Studia Sci. Math. Hungar. 31, 47-62 (1996)
    • (1996) Studia Sci. Math. Hungar. , vol.31 , pp. 47-62
    • Csáki, E.1    Salminen, P.2
  • 10
    • 0009253021 scopus 로고
    • The influence of the maximum term in the addition of independent random variables
    • Darling, D. A, The influence of the maximum term in the addition of independent random variables. Trans. Amer. Math. Soc. 73, 95-107 (1952)
    • (1952) Trans. Amer. Math. Soc. , vol.73 , pp. 95-107
    • Darling, D.A.1
  • 13
    • 0002434884 scopus 로고
    • Central limit theorem for nonstationary Markov chains I and II
    • Dobrushin, R. L., Central limit theorem for nonstationary Markov chains I and II, Theor. Probab. Appl. 1, 65-80, 329-383 (1956)
    • (1956) Theor. Probab. Appl. , vol.1 , pp. 65-80
    • Dobrushin, R.L.1
  • 16
    • 0039562708 scopus 로고
    • Theorems for the invariance principle type for recurrent semi-Markov processes with arbitrary phase space
    • Kaplan, E. I., and Silvestrov, D. S., Theorems for the invariance principle type for recurrent semi-Markov processes with arbitrary phase space. Theor. Probab. Appl. 24, 536-547 (1979)
    • (1979) Theor. Probab. Appl. , vol.24 , pp. 536-547
    • Kaplan, E.I.1    Silvestrov, D.S.2
  • 17
    • 0001442817 scopus 로고
    • Limit theorems for Lévy processes and Poisson point processes and their applications to Brownian excursions
    • Kasahara, Y., Limit theorems for Lévy processes and Poisson point processes and their applications to Brownian excursions. J. Math. Kyoto Univ. 24, 521-538 (1984)
    • (1984) J. Math. Kyoto Univ. , vol.24 , pp. 521-538
    • Kasahara, Y.1
  • 18
    • 84972560979 scopus 로고
    • A limit theorem for sums of random numbers of i.i.d. random variables and its application to occupation times of Markov chains
    • Kasahara, Y., A limit theorem for sums of random numbers of i.i.d. random variables and its application to occupation times of Markov chains. J. Math. Soc. Japan. 37, 197-205 (1985)
    • (1985) J. Math. Soc. Japan. , vol.37 , pp. 197-205
    • Kasahara, Y.1
  • 19
    • 53249119225 scopus 로고
    • Occupation times for Markov and semi-Markov chains
    • Kesten, H., Occupation times for Markov and semi-Markov chains. Trans. Amer. Math. Soc. 103, 82-112 (1962)
    • (1962) Trans. Amer. Math. Soc. , vol.103 , pp. 82-112
    • Kesten, H.1
  • 20
    • 0009295416 scopus 로고
    • On the global limit behaviour of Markov chains and of general nonsigular Markov processes
    • Krengel, U., On the global limit behaviour of Markov chains and of general nonsigular Markov processes. Z. Wahrs. verw Gebiete 6, 302-316 (1966)
    • (1966) Z. Wahrs. Verw Gebiete , vol.6 , pp. 302-316
    • Krengel, U.1
  • 21
    • 0000227816 scopus 로고
    • The range of stable random walks
    • Le Gall, J.-F. and Rosen, J., The range of stable random walks. Ann. Probab. 19, 650-705 (1991)
    • (1991) Ann. Probab. , vol.19 , pp. 650-705
    • Le Gall, J.-F.1    Rosen, J.2
  • 22
    • 0001232794 scopus 로고
    • Law of the iterated logarithm for the local times of symmetric Levy processes and recurrent random walks
    • Marcus, M. B. and Rosen, J., Law of the iterated logarithm for the local times of symmetric Levy processes and recurrent random walks. Ann. Probab. 22, 626-658 (1994)
    • (1994) Ann. Probab. , vol.22 , pp. 626-658
    • Marcus, M.B.1    Rosen, J.2
  • 23
    • 0000716092 scopus 로고
    • 2 and of Lévy processes and random walks in the domain of attraction of Cauchy random variables
    • 2 and of Lévy processes and random walks in the domain of attraction of Cauchy random variables. Ann. Inst. Henri Poincaré Probab. Statist. 30, 467-499 (1994)
    • (1994) Ann. Inst. Henri Poincaré Probab. Statist. , vol.30 , pp. 467-499
    • Marcus, M.B.1    Rosen, J.2
  • 25
    • 0000427555 scopus 로고
    • A splitting technique for Harris recurrent chains
    • Nummelin, E., A splitting technique for Harris recurrent chains. Z. Wahrs. verw Gebiete 43, 309-318 (1978)
    • (1978) Z. Wahrs. Verw Gebiete , vol.43 , pp. 309-318
    • Nummelin, E.1
  • 29
    • 0003737306 scopus 로고
    • North-Holland, New York
    • Revuz, D., Markov Chains. North-Holland, New York, 1975.
    • (1975) Markov Chains
    • Revuz, D.1
  • 31
    • 0000187468 scopus 로고
    • Loi functionelle du logarithme itéré pour les processus de Markov récurrents
    • Touati, A., Loi functionelle du logarithme itéré pour les processus de Markov récurrents. Ann. Probab. 18, 140-159 (1990)
    • (1990) Ann. Probab. , vol.18 , pp. 140-159
    • Touati, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.