Two-parameter semigroups, evolutions and their applications to Markov and diffusion fields on the plane. (1996) - Mishura, Yu.; Tomilov, Yu.
Abstract : We study two-parameter coordinate-wise C 0 -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.