Multiplicative ergodicity and large deviations for an irreducible Markov chain

Stochastic Processes and their Applications

Volumn 90, Issue 1, 2000, Pages 123-144

  Balaji, S ^a   Meyn, S P ^b  

^a NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Ergodic theory; Harmonic functions; Large deviations; Markov chain

Indexed keywords

EID: 0002801896     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(00)00032-6     Document Type: Article

References (18)

1. Arnold, L., Kliemann, W., 1987. Large deviations for linear Stochastic differential equations. In: Engelbrecht, J., Schmidt, W. (Eds.), Stochastic Differential Systems. Springer, Berlin, pp. 117-151.
2. Balaji, S., Borkar, V.S., Meyn, S.P., 1999. Risk sensitive dynamic programming with unbounded cost. Presented at the 38th IEEE Conference on Decision and Control, Pheonix, AZ, December 1999, and published in the proceedings.
3. Bolthausen, E., Deuschel, J.-D., Tamura, Y., 1995. Laplace approximations for large deviations of nonreversible Markov processes: the nondegenerate case. Ann. Probab. 23, 286-297.
4. Borkar, V.S., 1991. Topics in controlled Markov chains. Pitman Research Notes in Mathematics Series, Vol. 240. Longman Scientific & Technical, UK.
5. Borkar, V.S., Meyn, S.P., 1999. Risk Sensitive optimal control: existence and synthesis for models with unbounded cost. Math. Oper. Res., submitted.
6. de Acosta, A., 1990. Large deviations for empirical measures of Markov chains. J. Theoret. Probab. 3, 395-431.
7. Dembo, A., Zeitouni, O., 1993. Large Deviations Techniques and Applications. Jones and Bartlett Publishers, London, England.
8. Glynn, P.W., Meyn, S.P., 1996. A Liapunov bound for solutions of Poisson equation. Ann. Probab. 24, 916-931.
9. Kingman, J.F.C., 1973. Subadditive Ergodic theory. Ann. Probab. 1, 883-909.
10. Meyn, S.P., Tweedie, R.L., 1993. Markov Chains and Stochastic Stability. Springer, London.
11. Meyn, S.P., 1997. The policy improvement algorithm for Markov decision processes with general state space. IEEE Trans. Automat. Control AC-42, 191-196.
12. Ney, P., Nummelin, E., 1987a. Markov additive processes I: eigenvalue properties and limit theorems. Ann. Probab. 15, 561-592.
13. Ney, P., Nummelin, E., 1987b. Markov additive processes II: large deviations. Ann. Probab. 15, 593-609.
14. Nummelin, E., 1984. General Irreducible Markov Chains and Non-Negative Operators. Cambridge University Press, Cambridge, MA.
15. Pinsky, R.G., 1995. Positive Harmonic Functions and Diffusion. Cambridge University Press, Cambridge, UK.
16. Seneta, E., 1981. Non-Negative Matrices and Markov Chains, 2nd Edition. Springer, New York.
17. Varadhan, S.R.S., 1984. Large deviations and Applications. SIAM Publications, Philadelphia.
18. Whittle, P., 1990. Risk-Sensitive Optimal Control. Wiley, Chichester, NY.