Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 3, Pages 281-302
doi: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 Yu. Mishura and Yu. Tomilov. 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.