Renormalized Solutions for Stochastic Transport Equations and the Regularization by Bilinear Multiplicative Noise
By S. Attanasio, Franco Flandoli. 2010
69 citations recorded by the source corpus.
A linear stochastic transport equation with non-regular coefficients is considered. Under the same assumption of the deterministic theory, all weak L ∞-solutions are renormalized. But then, if the noise is non-degenerate, uniqueness of weak L ∞-solutions does not require essential new assumptions, opposite to the deterministic case where for instance the divergence of the drift is asked to be bounded. The proof gives a new explanation why bilinear multiplicative noise may have a regularizing effect.
Subfields: Applied Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/c787201610cd580a453427b82ed417050cec88f4
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In Applied Mathematics
- Massimiliano Gubinelli
- Lisa Beck
- M. Maurelli
- Franco Flandoli
- Lucio Galeati
- Feng-Yu Wang
- Samy Tindel
- Arnaud Debussche
In Finance
- Massimiliano Gubinelli
- Franco Flandoli
- Lisa Beck
- M. Maurelli
- Lucio Galeati
- Xicheng Zhang
- Martin Hairer
- Feng-Yu Wang
Citations in the corpus
- Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness (2014, methodology): “However, in [4] this approach has been applied directly to uniqueness of weak solutions so the renormalization step required weak differentiability of the drift.”