Optimal discretization of stochastic integrals driven by general Brownian semimartingale

Abstract : We study the optimal discretization error of stochastic integrals, driven by a multidimensional continuous Brownian semimartingale. In this setting we establish a pathwise lower bound for the renormalized quadratic variation of the error and we provide a sequence of discretiza- tion stopping times, which is asymptotically optimal. The latter is defined as hitting times of random ellipsoids by the semimartingale at hand. In comparison with previous available results, we allow a quite large class of semimartingales (relaxing in particular the non degeneracy conditions usually requested) and we prove that the asymptotic lower bound is attainable.
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Pré-publication, Document de travail
2017
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https://hal-polytechnique.archives-ouvertes.fr/hal-01241190
Contributeur : Emmanuel Gobet <>
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Dernière modification le : jeudi 10 mai 2018 - 02:04:17
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  • HAL Id : hal-01241190, version 2

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Emmanuel Gobet, Uladzislau Stazhynski. Optimal discretization of stochastic integrals driven by general Brownian semimartingale. 2017. 〈hal-01241190v2〉

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