1. The Itô-Tanaka Trick: a non-semimartingale approach.
- Author
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Coutin, Laure, Duboscq, Romain, and Réveillac, Anthony
- Subjects
SEMIMARTINGALES (Mathematics) ,WIENER processes ,RANDOM fields ,STOCHASTIC processes ,MARTINGALES (Mathematics) - Abstract
In this paper we provide an Itô-Tanaka trick formula in a non semimartingale context, filling a gap in the theory of regularisation by noise. In a classical Brownian framework, the Itô-Tanaka trick links the time average of a function f along the solution to a Brownian SDE, with the solution of a Fokker-Planck PDE. Our main contribution is to provide such a link in a non-semimartingale framework, where the solution to the non-available PDE is replaced by a well-chosen random field. This allows us to improve well-posedness results for fractional SDEs with a singular drift coefficient. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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