Conditions for recurrence and transience of a Markov chain on ℤ + and estimation of a geometric success probability

Annals of Statistics

Volumn 30, Issue 4, 2002, Pages 1214-1223

  Hobert, James P ^a   Schweinsberg, Jason ^b  

^a University of Florida   (United States)

^b Cornell University ^*  (United States)

Author keywords

Admissibility; Electrical network; Geometric distribution; Null recurrence; Reversibility; Weighted random walk

Indexed keywords

EID: 0036392232     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1031689024     Document Type: Article

References (12)

1. ABRAMOWITZ, M. and STEGUN, I. A. (1972). Handbook of Mathematical Functions. Dover, New York.
2. DOYLE, P. G. and SNELL, J. L. (1984). Random Walks and Electric Networks. Math. Assoc. Amer., Washington, DC.
3. DURRETT, R. (1996). Probability: Theory and Examples, 2nd ed. Duxbury Press, Belmont, CA.
4. EATON, M. L. (1992). A statistical diptych: Admissible inferences-recurrence of symmetric Markov chains. Ann. Statist. 20 1147-1179.
5. EATON, M. L. (1997). Admissibility in quadratically regular problems and recurrence of symmetric Markov chains: Why the connection? J. Statist. Plann. Inference 64 231-247.
6. HOBERT, J. P. and ROBERT, C. P. (1999). Baton's Markov chain, its conjugate partner and P-admissibility. Ann. Statist. 27 361-373.
7. KNOPP, K. (1990). Theory and Application of Infinite Series. Dover, New York.
8. LAMPERTI, J. (1960). Criteria for the recurrence or transience of stochastic processes, I. J. Math. Anal. Appl. 1 314-330.
9. LYONS, T. (1983). A simple criterion for transience of a reversible Markov chain. Ann. Probab. 11 393-402.
10. MCGUINNESS, S. (1991). Recurrent networks and a theorem of Nash-Williams. J. Theoret. Probab. 4 87-100.
11. NASH-WILLIAMS, C. ST. J. A. (1959). Random walk and electric currents in networks. Proc. Cambridge Philosophical Soc. 55 181-194.
12. PERES, Y. (1999). Probability on trees: An introductory climb. Lectures on Probability Theory and Statistics. Lecture Notes in Math. 1717 193-280. Springer, Berlin.