×

Some limit theorems for a general Markov process. (English) Zbl 0234.60086


MSC:

60J25 Continuous-time Markov processes on general state spaces
60F99 Limit theorems in probability theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Chacon, R. V., Identification of the limit of operator averages, J. Math. Mech., 11, 961-968 (1962) · Zbl 0139.34701
[2] Chacon, R. V.; Ornstein, D., A genreral ergodic theorem, Illinois J. Math., 4, 153-160 (1960) · Zbl 0134.12102
[3] Chung, K. L., Contributions to the theory of Markov chains II, Trans. Amer. math. Soc., 76, 397-419 (1954) · Zbl 0058.34602
[4] Chung, K. L., The general theory of Markov processes according to Doblin, Z. Wahrscheinlichkeits-theorie verw. Geb., 2, 230-254 (1964) · Zbl 0119.34604
[5] Chung, K. L., Markov chains with stationary transition probabilities (1960), Berlin-Göttingen-Heidelberg: Springer, Berlin-Göttingen-Heidelberg · Zbl 0092.34304
[6] Doblin, W., Eléments d’une théorie générale des chaines simples constantes de Markoff, Ann. sci. école norm, sup., III. Sér., 57, 61-111 (1940) · JFM 66.0617.01
[7] Doblin, W., Sur deux problèmes de M. Kolmogoroff concernant les chaÎnes denombrables, Bull. Soc. math. France, 66, 210-220 (1938) · JFM 64.0538.02
[8] Doob, J. L., Stochastic processes (1953), New York: Wiley and Sons, New York · Zbl 0053.26802
[9] Doob, J. L., Asymptotic properties of Markoff transitions probabilities, Trans. Amer. math. Soc., 63, 393-438 (1948) · Zbl 0041.45406
[10] Harris, T. E., Recurrent Markov processes II (abstract), Ann. math. Statistics, 26, 152-153 (1955)
[11] Harris, T. E., The existence of stationary measures for certain Markov processes, Proc. Third Berkeley Sympos. math. Statist. Probab., II, 113-124 (1956)
[12] Hopf, E., The general temporally discrete Markoff process, J. Math. Mech., 3, 13-45 (1954) · Zbl 0055.36705
[13] Jain, N. C.: Some limit theorems for a general Markov process. Doctoral dissertation submitted to the Department of Mathematics, Stanford University, 1965.
[14] Orey, S., Recurrent Markov chains, Pacific J. Math., 9, 805-827 (1959) · Zbl 0095.32902
[15] -, and B. Jamison: Tail σ-field of Markov processes recurrent in the sense of Harris. (To appear).
[16] Spitzer, F., Principles of random walk (1965), New York: Van Nostrand, New York · Zbl 0119.34304
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.