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Journal Articles Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Year : 2018

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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Dates and versions

hal-01241190 , version 1 (10-12-2015)
hal-01241190 , version 2 (08-11-2017)

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Emmanuel Gobet, Uladzislau Stazhynski. Optimal discretization of stochastic integrals driven by general Brownian semimartingale. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2018, 54 (3), ⟨10.1214/17-AIHP848⟩. ⟨hal-01241190v2⟩
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