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In this paper, following Nourdin-Peccati's methodology, we combine the Malliavin calculus and Stein's method to provide general bounds on the Wasserstein distance between the law of functionals of a compound Hawkes process and the one of a Gaussian random variable. To achieve this, we rely on the Poisson imbedding representation of a Hawkes process to provide a Malliavin calculus for the Hawkes processes, and more generally for compound Hawkes processes. As an application, we close a gap in the literature by providing a quantitative Central Limit Theorem for the compound Hawkes process. [ABSTRACT FROM AUTHOR]

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]

In this paper we address an open question formulated in [16] . That is, we extend the Itô–Tanaka trick, which links the time-average of a deterministic function f depending on a stochastic process X and F the solution of the Fokker–Planck equation associated to X , to random mappings f . To this end we provide new results on a class of adapted and non-adapted Fokker–Planck SPDEs and BSPDEs. [ABSTRACT FROM AUTHOR]

Abstract: We extend the work of Delong and Imkeller (2010)  concerning backward stochastic differential equations with time delayed generators (delay BSDEs). We give moment and a priori estimates in general -spaces and provide sufficient conditions for the solution of a delay BSDE to exist in . We introduce decoupled systems of SDEs and delay BSDEs (delay FBSDEs) and give sufficient conditions for their variational differentiability. We connect these variational derivatives to the Malliavin derivatives of delay FBSDEs via the usual representation formulas. We conclude with several path regularity results, in particular we extend the classic -path regularity to delay FBSDEs. [Copyright &y& Elsevier]

Abstract: In the framework of a nonparametric functional estimation for the drift of a Brownian motion we construct Stein type estimators of the form which are superefficient when is a superharmonic functional on the Wiener space for the Malliavin derivative D. To cite this article: N. Privault, A. Réveillac, C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]