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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]

Abstract: In this paper we give a central limit theorem for the weighted quadratic variation process of a two-parameter Brownian motion. As an application, we show that the discretized quadratic variations of a two-parameter diffusion observed on a regular grid form an asymptotically normal estimator of the quadratic variation of as goes to infinity. [Copyright &y& Elsevier]