Electronic Journal of Probability

Regularity of stochastic kinetic equations

Ennio Fedrizzi, Franco Flandoli, Enrico Priola, and Julien Vovelle

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 48, 42 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1496196076

Digital Object Identifier
doi:10.1214/17-EJP65

Mathematical Reviews number (MathSciNet)
MR3661662

Zentralblatt MATH identifier
1371.35372

Subjects
Primary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60H15: Stochastic partial differential equations [See also 35R60] 35R05: Partial differential equations with discontinuous coefficients or data 60H30: Applications of stochastic analysis (to PDE, etc.) 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Kinetic equation degenerate SDE regularization by noise hypoelliptic regularity

Rights
Creative Commons Attribution 4.0 International License.

Citation

Fedrizzi, Ennio; Flandoli, Franco; Priola, Enrico; Vovelle, Julien. Regularity of stochastic kinetic equations. Electron. J. Probab. 22 (2017), paper no. 48, 42 pp. doi:10.1214/17-EJP65. https://projecteuclid.org/euclid.ejp/1496196076


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