Geodesic
Stability of the nonlinear stochastic process approximizing a~system of interacted particles
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 400-409

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The nonlinear SDE of McKean–Vlasov type in the absence of external fields is considered. First, the existence and the uniqueness of the equation solution are proved. Next, the existence and the uniqueness of the stationary solution at the class of probability with fixed expectation are proved. Also, weak convergence to invariant probability is proved.
Keywords: nonlinear stochastic process, McKean–Vlasov equation, stability. 
@article{TVP_2006_51_2_a10,
     author = {P. N. Yarykin},
     title = {Stability of the nonlinear stochastic process approximizing a~system of interacted particles},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {400--409},
     publisher = {mathdoc},
     volume = {51},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_2_a10/}
}
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P. N. Yarykin. Stability of the nonlinear stochastic process approximizing a~system of interacted particles. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 400-409. http://geodesic.mathdoc.fr/item/TVP_2006_51_2_a10/