The note provides the relation between symmetries and first integrals of It\^{o} stochastic differential equations and symmetries of the associated Kolmogorov backward equation. Relation between the symmetries of the Kolmogorov backward equation and the symmetries of the Kolmogorov forward equation is also given.
Symmetries and first integrals for variational ODEs with delay
The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction
Stochastic spikes and strong noise limits of stochastic differential equations
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