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2017 On explicit approximations for Lévy driven SDEs with super-linear diffusion coefficients
Chaman Kumar, Sotirios Sabanis
Electron. J. Probab. 22: 1-19 (2017). DOI: 10.1214/17-EJP89

Abstract

Motivated by the results of [21], we propose explicit Euler-type schemes for SDEs with random coefficients driven by Lévy noise when the drift and diffusion coefficients can grow super-linearly. As an application of our results, one can construct explicit Euler-type schemes for SDEs with delays (SDDEs) which are driven by Lévy noise and have super-linear coefficients. Strong convergence results are established and their rate of convergence is shown to be equal to that of the classical Euler scheme. It is proved that the optimal rate of convergence is achieved for $\mathcal{L} ^2$-convergence which is consistent with the corresponding results available in the literature.

Citation

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Chaman Kumar. Sotirios Sabanis. "On explicit approximations for Lévy driven SDEs with super-linear diffusion coefficients." Electron. J. Probab. 22 1 - 19, 2017. https://doi.org/10.1214/17-EJP89

Information

Received: 10 January 2017; Accepted: 4 August 2017; Published: 2017
First available in Project Euclid: 13 September 2017

zbMATH: 1379.60076
MathSciNet: MR3698742
Digital Object Identifier: 10.1214/17-EJP89

Subjects:
Primary: 60H35
Secondary: 65C30

JOURNAL ARTICLE
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