Open Access
2017 Regularity of stochastic kinetic equations
Ennio Fedrizzi, Franco Flandoli, Enrico Priola, Julien Vovelle
Electron. J. Probab. 22: 1-42 (2017). DOI: 10.1214/17-EJP65


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 study the related degenerate Kolmogorov equation in Bessel-Sobolev spaces and construct a suitable stochastic flow.


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Ennio Fedrizzi. Franco Flandoli. Enrico Priola. Julien Vovelle. "Regularity of stochastic kinetic equations." Electron. J. Probab. 22 1 - 42, 2017.


Received: 12 June 2016; Accepted: 3 May 2017; Published: 2017
First available in Project Euclid: 31 May 2017

zbMATH: 1371.35372
MathSciNet: MR3661662
Digital Object Identifier: 10.1214/17-EJP65

Primary: 35R05 , 35R60 , 60H10 , 60H15 , 60H30

Keywords: degenerate SDE , hypoelliptic regularity , Kinetic equation , Regularization by noise

Vol.22 • 2017
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