Processes with infinitely many jumping particles

Sullivan, Wayne G.

doi:10.1090/S0002-9939-1976-0394940-6

Processes with infinitely many jumping particles
HTML articles powered by AMS MathViewer

by Wayne G. Sullivan PDF

Proc. Amer. Math. Soc. 54 (1976), 326-330 Request permission

Abstract:

We give sufficient conditions for a Markov process of an infinite particle system to be specified by a formal generator which has a term for each finite subset of particles. Under stronger assumptions we show that processes of this type preserve a certain property of probability measures.

References

R. L. Dobrušin, Markov processes with a large number of locally interacting components: The invertible case and certain generalizations, Problemy Peredači Informacii 7 (1971), no. 3, 57–66 (Russian). MR 0311000
Richard Holley, Markovian interaction processes with finite range interactions, Ann. Math. Statist. 43 (1972), 1961–1967. MR 373070, DOI 10.1214/aoms/1177690867
Thomas M. Liggett, Existence theorems for infinite particle systems, Trans. Amer. Math. Soc. 165 (1972), 471–481. MR 309218, DOI 10.1090/S0002-9947-1972-0309218-7
H. R. Pitt, Some generalizations of the ergodic theorem, Proc. Cambridge Philos. Soc. 38 (1942), 325–343. MR 7947
Frank Spitzer, Interaction of Markov processes, Advances in Math. 5 (1970), 246–290 (1970). MR 268959, DOI 10.1016/0001-8708(70)90034-4
F. Spitzer, Random fields and interacting particle systems, Mathematical Association of America, Washington, D.C., 1971. Notes on lectures given at the 1971 MAA Summer Seminar, Williams College, Williamstown, Mass. MR 0381041
Wayne G. Sullivan, A unified existence and ergodic theorem for Markov evolution of random fields, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 31 (1974/75), 47–56. MR 375534, DOI 10.1007/BF00538715

Additional Information

Journal: Proc. Amer. Math. Soc. 54 (1976), 326-330
DOI: https://doi.org/10.1090/S0002-9939-1976-0394940-6
MathSciNet review: 0394940