Geodesic
Transformation of one-dimensional diffusion fields in the plane
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 3, pp. 565-577

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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, bidirected diffusion fields, the Itô, invariance problem.
Mots-clés : equivalent diffusion fields, formula 
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     author = {I. D. Cherkasov},
     title = {Transformation of one-dimensional diffusion fields in the plane},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {565--577},
     publisher = {mathdoc},
     volume = {40},
     number = {3},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_3_a6/}
}
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I. D. Cherkasov. Transformation of one-dimensional diffusion fields in the plane. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 3, pp. 565-577. http://geodesic.mathdoc.fr/item/TVP_1995_40_3_a6/