×

zbMATH — the first resource for mathematics

Random invariant measures for Markov chains and independent particle systems. (English) Zbl 0373.60076

MSC:
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60B10 Convergence of probability measures
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Choquet, G. and Deny, J.: Sur l’?quation de convolution ?=?*?. C.R. Acad. Sci. Paris 250, 799-801 (1960) · Zbl 0093.12802
[2] Cox, T.: Entrance Laws for Markov Chains. Ann. Probability 5, 533-549 (1977) · Zbl 0369.60079 · doi:10.1214/aop/1176995759
[3] Dobrushin, R.L.: On Poisson Laws for Distributions of Particles in Space (in Russian). Ukrain. Math. Z. 8, 127-134 (1956)
[4] Doob, J.L.: Stochastic Processes. New York: John Wiley 1953 · Zbl 0053.26802
[5] Dynkin, E.B.: Sufficient Statistics and Extreme Points. (To appear) · Zbl 0403.62009
[6] Kallenberg, O.: Random Measures. London: Academic Press 1976 · Zbl 0345.60032
[7] Lewis, P., editor: Stochastic Point Processes: Statistical Analysis, Theory, and Applications. New York: John Wiley and Sons 1972 · Zbl 0238.00014
[8] Liggett, T.: The Stochastic Evolution of Infinite Systems of Interacting Particles. Lecture Notes in Math. 598. Berlin Heidelberg New York: Springer 1977 · Zbl 0363.60109
[9] Matthes, K.: Infinitely Divisible Point Processes, 384-404, in Lewis [7] · Zbl 0267.60060
[10] Neveu, J.: Mathematical Foundations of the Calculus of Probability. San Francisco: Holden Day 1965 · Zbl 0137.11301
[11] Revuz, D.: Markov Chains. Amsterdam: North Holland 1975 · Zbl 0332.60045
[12] Spitzer, F.: Interaction of Markov Processes. Advances in Math. 5, 246-290 (1970) · Zbl 0312.60060 · doi:10.1016/0001-8708(70)90034-4
[13] Stone, C.: On a Theorem of Dobrushin. Ann. Math. Statist. 39, 1391-1401 (1968) · Zbl 0269.60045 · doi:10.1214/aoms/1177698327
[14] Stone, C.: Ratio Limit Theorems for Random Walks on Groups. Trans. Amer. Math. Soc. 125. 86-100 (1966) · Zbl 0168.38501 · doi:10.1090/S0002-9947-1966-0217887-2
[15] Fichtner, K.: Gleichverteilungseigenschaften substochasticher Kerne und zuf?llige Punktfolgen. Math. Nachr. 62, 251-260 (1974) · Zbl 0291.60032 · doi:10.1002/mana.3210620122
[16] Kerstan, J., Matthes, K., Mecke, J.: Unbegrenzte teilbare Punktprozesse. Berlin: Akademie-Verlag 1974
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.