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Intégrales stochastiques de processus anticipants et projections duales prévisibles.

Catherine Donati-Martin, Marc Yor (1999)

Publicacions Matemàtiques

We define a stochastic anticipating integral δμ with respect to Brownian motion, associated to a non adapted increasing process (μt), with dual projection t. The integral δμ(u) of an anticipating process (ut) satisfies: for every bounded predictable process ft,E [ (∫ fsdBs ) δμ(u) ] = E [ ∫ fsusdμs ].We characterize this integral when μt = supt ≤s ≤ 1 Bs. The proof relies on a path decomposition of Brownian motion up to time 1.

Irregular sampling and central limit theorems for power variations : the continuous case

Takaki Hayashi, Jean Jacod, Nakahiro Yoshida (2011)

Annales de l'I.H.P. Probabilités et statistiques

In the context of high frequency data, one often has to deal with observations occurring at irregularly spaced times, at transaction times for example in finance. Here we examine how the estimation of the squared or other powers of the volatility is affected by irregularly spaced data. The emphasis is on the kind of assumptions on the sampling scheme which allow to provide consistent estimators, together with an associated central limit theorem, and especially when the sampling scheme depends on...

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