Two-parameter semigroups, evolutions and their applications to Markov and diffusion fields on the plane. (1996)

• Record Type: Journal Article
• Authors: Mishura, Yu.; Tomilov, Yu.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 9:Number 3(1996)
• Page Start: 281
• Page End: 302
• Publication Date: 1996
• Subjects: two-parameter semigroup -- two-parameter evolution operator -- Markov field -- diffusion field; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953396000275
• Languages: English
• ISSNs: 1048-9533

Abstract

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.