@article{AIHPB_2004__40_1_89_0, author = {Chen, Xia and Guillin, Arnaud}, title = {The functional moderate deviations for {Harris} recurrent {Markov} chains and applications}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {89--124}, publisher = {Elsevier}, volume = {40}, number = {1}, year = {2004}, doi = {10.1016/j.anihpb.2003.07.002}, mrnumber = {2037475}, zbl = {1035.60021}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpb.2003.07.002/} }
TY - JOUR AU - Chen, Xia AU - Guillin, Arnaud TI - The functional moderate deviations for Harris recurrent Markov chains and applications JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2004 SP - 89 EP - 124 VL - 40 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpb.2003.07.002/ DO - 10.1016/j.anihpb.2003.07.002 LA - en ID - AIHPB_2004__40_1_89_0 ER -
%0 Journal Article %A Chen, Xia %A Guillin, Arnaud %T The functional moderate deviations for Harris recurrent Markov chains and applications %J Annales de l'I.H.P. Probabilités et statistiques %D 2004 %P 89-124 %V 40 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpb.2003.07.002/ %R 10.1016/j.anihpb.2003.07.002 %G en %F AIHPB_2004__40_1_89_0
Chen, Xia; Guillin, Arnaud. The functional moderate deviations for Harris recurrent Markov chains and applications. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 1, pp. 89-124. doi : 10.1016/j.anihpb.2003.07.002. http://www.numdam.org/articles/10.1016/j.anihpb.2003.07.002/
[1] Large deviations for vector-valued functional of Markov chain: lower bounds, Ann. Probab. 16 (1988) 925-960. | MR | Zbl
,[2] Moderate deviations for empirical measures of Markov chains: lower bounds, Ann. Probab. 25 (1997) 259-284. | MR | Zbl
,[3] Moderate deviations for empirical measures of Markov chains: upper bounds, J. Theoret. Probab. 11 (1998) 1075-1110. | MR | Zbl
, ,[4] A new approach to the limit theory of recurrent Markov chains, Trans. Amer. Math. Soc. 245 (1978) 493-501. | MR | Zbl
, ,[5] Propriétés relatives des processus de Markov récurrents, Z. Wahr. Geb. 13 (1969) 286-314. | MR | Zbl
, , ,[6] Limit theorems for functionals of ergodic Markov chains with general state space, Mem. Amer. Math. Soc. 139 (664) (1999). | MR | Zbl
,[7] The law of the iterated logarithm for functionals of Harris recurrent Markov chains: self normalization, J. Theoret. Probab. 12 (1999) 421-445. | MR | Zbl
,[8] How often does a Harris recurrent Markov chain recur?, Ann. Probab. 27 (1999) 1324-1346. | MR | Zbl
,[9] On the limit laws of the second order for additive functionals of Harris recurrent Markov chains, Probab. Theory Related Fields 116 (2000) 89-123. | MR | Zbl
,[10] Moderate deviations for Markovian occupation times, Stochastic Process. Appl. 94 (2001) 51-70. | MR | Zbl
,[11] On the zeros of ∑1n±1, Ann. of Math. 50 (1949) 385-400. | Zbl
, ,[12] On additive functionals of Markov chains, J. Theoret. Probab. 8 (1995) 905-919. | MR | Zbl
, ,[13] On the additive functionals of diffussion processes, Studia Sci. Math. Hungar. 31 (1996) 47-62. | MR | Zbl
, ,[14] Self-normalized moderate deviations and LILs, Stochastic Process. Appl. 75 (1998) 51-65. | MR | Zbl
, ,[15] Large Deviations Techniques and Applications, Jones and Bartlett, Boston, 1993. | MR | Zbl
, ,[16] Large and moderate deviations for quadratic empirical processes, Stat. Inf. Stoch. Proc. 2 (1999) 195-225. | MR | Zbl
, , ,[17] Moderate deviations of Markov Chains with atom, Stochastic Process. Appl. 95 (2001) 203-217. | MR | Zbl
, ,[18] Random Iterative Models, Springer, New York, 1997. | MR | Zbl
,[19] Some problems concerning the structure of random walks, Acta Math. 11 (1960) 137-162. | MR | Zbl
, ,[20] Large and moderate deviations for the local time of a recurrent Markov chain on Z2, Ann. Inst. H. Poinc. (Probab. Statist.) 34 (1998) 687-704. | Numdam | MR | Zbl
, ,[21] Uniform moderate deviations of functional empirical processes of Markov chains, Probab. Math. Stat. 20 (2000) 237-260. | MR | Zbl
,[22] Asymptotic behavior for the local time of a recurrent random walk, Ann. Probab. 11 (1983) 64-85. | MR | Zbl
, ,[23] Laws of large numbers and moderate deviations for stochastic processes with stationary and independent increments, Stochastic Process. Appl. 44 (1993) 205-219. | MR | Zbl
, , , ,[24] An iterated logarithm law for local times, Duke Math. J. 32 (1965) 447-456. | MR | Zbl
,[25] The range of stable random walks, Ann. Probab. 19 (1991) 650-705. | MR | Zbl
, ,[26] Markov Chains and Stochastic Stability, Springer-Verlag, London, 1993. | MR | Zbl
, ,[27] Law of the iterated logarithm for the local times of symmetric Lévy processes and recurrent random walks, Ann. Probab. 22 (1994) 626-658. | MR | Zbl
, ,[28] A splitting technique for Harris recurrent chains, Z. Wahr. Geb. 43 (1978) 309-318. | MR | Zbl
,[29] General Irreducible Markov Chains and Non-negative Operators, Cambridge University Press, Cambridge, 1984. | MR | Zbl
,[30] Limit Theorems for Markov Chain Transition Probabilities, Van Nostrand Reinhold, London, 1971. | MR | Zbl
,[31] Random Walk in Random and Non-random Environments, World Scientific, London, 1990. | MR | Zbl
,[32] An invariance principle for the law of the iterated logarithm, Z. Wahr. Geb. 3 (1964) 211-226. | MR | Zbl
,[33] Markov Chains, North-Holland, New York, 1975. | MR | Zbl
,[34] Loi fonctionnelle du logarithme itéré pour les processus de Markov récurrents, Ann. Probab. 18 (1990) 140-159. | MR | Zbl
,[35] Moderate deviations for random variables related to CLT, Ann. Probab. 23 (1995) 420-445. | MR | Zbl
,Cité par Sources :