Electronic Journal of Probability

On explicit approximations for Lévy driven SDEs with super-linear diffusion coefficients

Chaman Kumar and Sotirios Sabanis

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 73, 19 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1505268104

Digital Object Identifier
doi:10.1214/17-EJP89

Mathematical Reviews number (MathSciNet)
MR3698742

Zentralblatt MATH identifier
1379.60076

Subjects
Primary: 60H35: Computational methods for stochastic equations [See also 65C30]
Secondary: 65C30: Stochastic differential and integral equations

Keywords
explicit Euler-type scheme super-linear drift and diffusion coefficients SDE driven by Lévy noise random coefficients strong convergence delay equations

Rights
Creative Commons Attribution 4.0 International License.

Citation

Kumar, Chaman; Sabanis, Sotirios. On explicit approximations for Lévy driven SDEs with super-linear diffusion coefficients. Electron. J. Probab. 22 (2017), paper no. 73, 19 pp. doi:10.1214/17-EJP89. https://projecteuclid.org/euclid.ejp/1505268104


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