Geodesic
On small random perturbations of a~second order differential equation
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 505-514

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The paper deals with limiting behaviour of an invariant measure of the diffusion process obtained on the plane when a dynamical system corresponding to some second order differential equation is disturbed by white noise with a small coefficient. It is shown that the theorem proved in the case of a non-degenerate process on a compact manifold in [1] is also true (with certain changes) in the case under consideration. 
@article{TVP_1973_18_3_a5,
     author = {V. N. Dubrovsky},
     title = {On small random perturbations of a~second order differential equation},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {505--514},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a5/}
}
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V. N. Dubrovsky. On small random perturbations of a~second order differential equation. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 505-514. http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a5/