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Regularity of stochastic kinetic equations

Ennio Fedrizzi, Franco Flandoli, Enrico Priola, Julien Vovelle
2017 Electronic Journal of Probability  
We consider regularity properties of stochastic kinetic equations with multiplicative noise and drift term which belongs to a space of mixed regularity (L p -regularity in the velocity-variable and Sobolev regularity in the space-variable). We prove that, in contrast with the deterministic case, the SPDE admits a unique weakly differentiable solution which preserves a certain degree of Sobolev regularity of the initial condition without developing discontinuities. To prove the result we also
more » ... e result we also study the related degenerate Kolmogorov equation in Bessel-Sobolev spaces and construct a suitable stochastic flow.
doi:10.1214/17-ejp65 fatcat:6fmcor54xfewtb3et2jph76h7u