Wellposedness for stochastic continuity equations with Ladyzhenskaya–Prodi–Serrin condition
By Wladimir A. P. Neves, Christian Olivera. 2013
54 citations recorded by the source corpus.
We consider the stochastic divergence-free continuity equations with Ladyzhenskaya–Prodi–Serrin condition. Wellposedness is proved meanwhile uniqueness may fail for the deterministic PDE. The main issue of strong uniqueness, in the probabilistic sense, relies on stochastic characteristic method and the generalized Itô–Wentzell–Kunita formula. The stability property for the unique solution is proved with respect to the initial data. Moreover, a persistence result is established by a representation formula.
Subfields: Applied Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/62409447b016f41273139d58195b5003cbf950b3
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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): “In [41] the case of Hölder continuous bounded drift is treated, by means of the differentiable flow associated to the sDE; [66] extends the result and the approach to drifts in KR class with zero divergence.”