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Teoriya Veroyatnostei i ee Primeneniya, 1995, Volume 40, Issue 3, Pages 565–577 (Mi tvp3455)  
Transformation of one-dimensional diffusion fields in the plane

I. D. Cherkasov

Saratov State University named after N. G. Chernyshevsky
Full-text PDF (688 kB)
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, Volume 40, Issue 3, Pages 446–455
DOI: https://doi.org/10.1137/1140049
Bibliographic databases:
Language: Russian
Citation: I. D. Cherkasov, “Transformation of one-dimensional diffusion fields in the plane”, Teor. Veroyatnost. i Primenen., 40:3 (1995), 565–577; Theory Probab. Appl., 40:3 (1995), 446–455
Citation in format AMSBIB
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\vol 40
\issue 3
\pages 565--577
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\transl
\jour Theory Probab. Appl.
\yr 1995
\vol 40
\issue 3
\pages 446--455
\crossref{https://doi.org/10.1137/1140049}
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