Geodesic
The superposition principle for Fokker--Planck--Kolmogorov equations with unbounded coefficients
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 4, pp. 59-79

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The superposition principle delivers a probabilistic representation of a solution\break $\{\mu_t\}_{t\in[0, T]}$ of the Fokker–Planck–Kolmogorov equation $\partial_t\mu_t=L^{*}\mu_t$ in terms of a solution $P$ of the martingale problem with operator $L$. We generalize the superposition principle to the case of equations on a domain, examine the transformation of the measure $P$ and the operator $L$ under a change of variables, and obtain new conditions for the validity of the superposition principle under the assumption of the existence of a Lyapunov function for the unbounded part of the drift coefficient.
Mots-clés : Fokker–Planck–Kolmogorov equation, superposition principle. 
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     author = {T. I. Krasovitskii and S. V. Shaposhnikov},
     title = {The superposition principle for {Fokker--Planck--Kolmogorov} equations with unbounded coefficients},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {56},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_4_a5/}
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T. I. Krasovitskii; S. V. Shaposhnikov. The superposition principle for Fokker--Planck--Kolmogorov equations with unbounded coefficients. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 4, pp. 59-79. http://geodesic.mathdoc.fr/item/FAA_2022_56_4_a5/