## Electronic Journal of Probability

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

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

Chaman Kumar and Sotirios Sabanis

#### 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