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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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https://hal-polytechnique.archives-ouvertes.fr/hal-01241190
Contributor : Emmanuel Gobet <>
Submitted on : Wednesday, November 8, 2017 - 9:18:17 PM
Last modification on : Tuesday, September 22, 2020 - 3:52:18 AM
Long-term archiving on: : Friday, February 9, 2018 - 2:02:39 PM

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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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