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Regularity of solutions to Kolmogorov equations with perturbed drifts
Vladimir I. Bogachev, Egor D. Kosov, Alexander V. Shaposhnikov
We prove that a probability solution of the stationary Kolmogorov equation generated by a first order perturbation of the Ornstein--Uhlenbeck operator possesses a highly in…
Pathwise vs. path-by-path uniqueness
Alexander Shaposhnikov, Lukas Wresch
We construct a series of stochastic differential equations of the form which exhibit nonuniqueness in the path-by-path sense while having a unique adap…
Log-Sobolev-type inequalities for solutions to stationary Fokker-Planck-Kolmogorov equations
V. I. Bogachev, A. V. Shaposhnikov, S. V. Shaposhnikov
We prove that every probability measure satisfying the stationary Fokker-Planck-Kolmogorov equation obtained by a -integrable perturbation of the drift term of the…
Correction to the paper "Some remarks on Davie's uniqueness theorem"
A. V. Shaposhnikov
The property 4 in Proposition 2.3 from the paper "Some remarks on Davie's uniqueness theorem" is replaced with a weaker assertion which is sufficient for the proof of the main resu…