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Linear information for approximation of the Itô integrals

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Abstract

We study optimal approximation of stochastic integrals in the Itô sense when linear information, consisting of certain integrals of trajectories of Brownian motion, is available. Upper bounds on the nth minimal error, where n is the fixed cardinality of information, are obtained by the Wagner–Platen algorithm and are O(n  − 3/2) or O(n  − 2), depending on considered class of integrands. We also show that Ω(n  − 2) is a lower bound which holds even for very smooth integrands.

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Authors and Affiliations

  1. Department of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Cracow, Poland

    Paweł Przybyłowicz

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  1. Paweł Przybyłowicz
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Correspondence to Paweł Przybyłowicz.

Additional information

This research was partly supported by AGH grant No. 10.420.03.

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Przybyłowicz, P. Linear information for approximation of the Itô integrals. Numer Algor 52, 677–699 (2009). https://doi.org/10.1007/s11075-009-9307-y

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  • DOI: https://doi.org/10.1007/s11075-009-9307-y

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