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Optimal global approximation of stochastic differential equations with additive Poisson noise

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Abstract

We consider strong global approximation of SDEs driven by a homogeneous Poisson process with intensity λ > 0. We establish the exact convergence rate of minimal errors that can be achieved by arbitrary algorithms based on a finite number of observations of the Poisson process. We consider two classes of methods using equidistant or nonequidistant sampling of the Poisson process, respectively. We provide a construction of optimal schemes, based on the classical Euler scheme, which asymptotically attain the established minimal errors. It turns out that methods based on nonequidistant mesh are more efficient than those based on the equidistant mesh.

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Authors and Affiliations

  1. Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Krakow, 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 the Polish NCN grant - decision No. DEC-2013/09/B/ST1/04275 and by AGH local grant.

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Przybyłowicz, P. Optimal global approximation of stochastic differential equations with additive Poisson noise. Numer Algor 73, 323–348 (2016). https://doi.org/10.1007/s11075-016-0097-8

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  • DOI: https://doi.org/10.1007/s11075-016-0097-8

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