Geodesic
Numerical solution to stochastic differential equations with growing variance
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 1, pp. 1-10

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The paper considers a new method for transition from an initial unstable in the mean square SDE system to the SDE system with a solution close to a stationary process. The SDE systems for a stochastic component are obtained with the use of the Ito formula both in the case of linear and nonlinear initial SDE systems. 
@article{SJVM_2005_8_1_a0,
     author = {T. A. Averina and S. S. Artem'ev},
     title = {Numerical solution to stochastic differential equations with growing variance},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {1--10},
     publisher = {mathdoc},
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     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2005_8_1_a0/}
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T. A. Averina; S. S. Artem'ev. Numerical solution to stochastic differential equations with growing variance. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 1, pp. 1-10. http://geodesic.mathdoc.fr/item/SJVM_2005_8_1_a0/