Geodesic
On a transformation of systems of stochastic differential equations
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 4, pp. 748-751

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For a diffusion Markov process defined by the Ito equations (1), an $\mathfrak{F}_t$-measurable transformation defined by (3) or (4) with $G(z,t)$ and $F(x,t)$ satisfying (2) and (6) respectively is considered. The process $(z(t), y(t))$ where $z(t)=F(x(t), t)$ with $(x(t), y(t))$ defined by (1) is shown to satisfy the system (5). 
@article{TVP_1972_17_4_a13,
     author = {V. A. Lebedev},
     title = {On a transformation of systems of stochastic differential equations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {748--751},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a13/}
}
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V. A. Lebedev. On a transformation of systems of stochastic differential equations. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 4, pp. 748-751. http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a13/