Abstract
Random fields that have the “coordinatewise” Markov property are considered. The notions of an excessive function, a potential, and a continuous additive functional are introduced. Sufficient conditions for the existence of local time as a special form of continuous additive functional are formulated, and the uniqueness of this time to within a multiplicative constant is proved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Cairoli and J. B. Walsh, “Stochastic integrals in the plane,”Acta Math.,134, No. 1–2, 111–183 (1975).
I. I. Gikhman and A. V. Skorokhod,Theory of Stochastic Processes [in Russian], Vol. 2, Nauka, Moscow (1973).
G. Mazziotto, E. Merzbach, and J. Szpirglas, “Discontinuités des processus croissants et martingales à variation intégrable,”Springer Lect. Notes Math.,863, 59–83 (1981).
R. M. Blumenthal and R. K. Getoor,Markov Processes and Potential Theory, Academic Press, New York (1968).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 56–63, January, 1995.
Rights and permissions
About this article
Cite this article
Mishura, Y.S. Existence and properties of local times for Markov random fields. Ukr Math J 47, 63–73 (1995). https://doi.org/10.1007/BF01058796
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058796