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Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 3, Pages 281-302
http://dx.doi.org/10.1155/S1048953396000275

Two-parameter semigroups, evolutions and their applications to Markov and diffusion fields on the plane

Kiev University, Department of Mathematics, Kiev 252601, Ukraine

Received 1 February 1995; Revised 1 December 1995

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study two-parameter coordinate-wise C0-semigroups and their generators, as well as two-parameter evolutions and differential equations up to the second order for them. These results are applied to obtain the Hille-Yosida theorem for homogeneous Markov fields of the Feller type and to establish forward, backward, and mixed Kolmogorov equations for nonhomogeneous diffusion fields on the plane.