Restoration of Well-Posedness of Infinite-Dimensional Singular ODE’s via Noise-Reference-Cited by-同舟云学术

Restoration of Well-Posedness of Infinite-Dimensional Singular ODE’s via Noise

Published:2023-03-07 Issue: Volume: Page:
ISSN:0926-2601
Container-title:Potential Analysis
language:en
Short-container-title:Potential Anal

Author:

Baños David^ORCID,Bauer Martin,Meyer-Brandis Thilo,Proske Frank

Abstract

AbstractIn this paper we aim at generalizing the results of A. K. Zvonkin (That removes the drift, 22, 129, 41) and A. Y. Veretennikov (Theory Probab. Appl., 24, 354, 39) on the construction of unique strong solutions of stochastic differential equations with singular drift vector field and additive noise in the Euclidean space to the case of infinite-dimensional state spaces. The regularizing driving noise in our equation is chosen to be a locally non-Hölder continuous Hilbert space valued process of fractal nature, which does not allow for the use of classical construction techniques for strong solutions from PDE or semimartingale theory. Our approach, which does not resort to the Yamada-Watanabe principle for the verification of pathwise uniqueness of solutions, is based on Malliavin calculus.

Funder

University of Oslo

Publisher

Springer Science and Business Media LLC

Subject

Analysis

Link

https://link.springer.com/content/pdf/10.1007/s11118-023-10069-6.pdf

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