Electronic Journal of Probability
- Electron. J. Probab.
- Volume 22 (2017), paper no. 48, 42 pp.
Regularity of stochastic kinetic equations
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.
Electron. J. Probab., Volume 22 (2017), paper no. 48, 42 pp.
Received: 12 June 2016
Accepted: 3 May 2017
First available in Project Euclid: 31 May 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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