Regularization effects of a noise propagating through a chain of differential equations: an almost sharp result
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- by Paul-Éric Chaudru de Raynal and Stéphane Menozzi PDF
- Trans. Amer. Math. Soc. 375 (2022), 1-45 Request permission
Abstract:
We investigate the effects of the propagation of a non-degenerate Brownian noise through a chain of deterministic differential equations whose coefficients are rough and satisfy a weak like Hörmander structure (i.e. a non-degeneracy condition w.r.t. the components which transmit the noise). In particular we characterize, through suitable counter-examples, almost sharp regularity exponents that ensure that weak well posedness holds for the associated SDE. As a by-product of our approach, we also derive some density estimates of Krylov type for the weak solutions of the considered SDEs.References
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Additional Information
- Paul-Éric Chaudru de Raynal
- Affiliation: Univ. Savoie Mont Blanc, CNRS, LAMA, F-73000 Chambéry, France
- MR Author ID: 1100135
- Email: pe.deraynal@univ-smb.fr
- Stéphane Menozzi
- Affiliation: Laboratoire de Modélisation Mathématique d’Evry (LaMME), Université d’Evry Val d’Essonne, 23 Boulevard de France 91037 Evry, France; and Laboratory of Stochastic Analysis, HSE, Shabolovka 31, Moscow, Russian Federation
- MR Author ID: 739222
- Email: stephane.menozzi@univ-evry.fr
- Received by editor(s): October 9, 2017
- Received by editor(s) in revised form: November 28, 2018
- Published electronically: November 5, 2021
- Additional Notes: For the second author, the article was prepared within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program.
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 1-45
- MSC (2020): Primary 60H10, 34F05; Secondary 60H30
- DOI: https://doi.org/10.1090/tran/7947
- MathSciNet review: 4358660