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

Yu. Mishura and Yu. Tomilov

 Kiev University, Department of Mathematics, Kiev 252601, Ukraine
Received 1 February 1995; Revised 1 December 1995

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.