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

[摘要] We study two-parameter coordinate-wiseC0-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.

[学科分类] 应用数学