zbMATH — the first resource for mathematics

Transformation of one-dimensional diffusion fields on the plane. (Russian) Zbl 0647.60059
The diffusion Markov fields \(\xi(z)\), \(z\in R^ 2_+\), considered in this paper are obtained as solutions of suitable classes of stochastic differential equations involving stochastic integrals with respect to the two-parameter Wiener process.
The author has found conditions for two diffusion fields to be equivalent. He answers questions of how to transform a diffusion field into a Gaussian martingale, and in particular, how to get a two-parameter Wiener process from a diffusion field. The Ito formula is used to establish an invariant representation for diffusion fields. Finally, results are given for the transition probabilities and the corresponding densities of diffusion random fields.
Reviewer: J.M.Stoyanov
60G60 Random fields
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes