Two‐parameter semigroups, evolutions and their applications to Markov and diffusion fields on the plane
Анотація
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.
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