Transformation of one-dimensional diffusion fields in the plane

I. D. Cherkasov

Saratov State University named after N. G. Chernyshevsky

Abstract: Necessary and sufficient conditions are given for the possibility of a diffusion field defined by diffusion and transfer coefficients to be transformed into another field. The problem of transforming a diffusion field into a Gaussian continuous square integrable martingale and, in particular, into a Wiener field is investigated in detail.

Keywords: conditional independence of $\sigma$-algebras, Gaussian strong continuous martingales, square integrable martingales, Wiener fields, stochastic differential equations, equivalent diffusion fields, bidirected diffusion fields, the Itô, formula, invariance problem.

Received: 21.07.1987
Revised: 27.04.1994

 English version: Theory of Probability and its Applications, 1995, 40:3, 446–455

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