American Institute of Mathematical Sciences

March  2021, 26(3): 1405-1446. doi: 10.3934/dcdsb.2020167

On Milstein-type scheme for SDE driven by Lévy noise with super-linear coefficients

 Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India, 247 667

* Corresponding author: C. Kumar (chaman.kumar@ma.iitr.ac.in)

Received  July 2019 Revised  December 2019 Published  May 2020

Fund Project: The author is supported by Professional Development Allowance (PDA) and Faculty Initiation Grant provided by the Indian Institute of Technology Roorkee

A new explicit Milstein-type scheme for SDE driven by Lévy noise is proposed where both drift and diffusion coefficients are allowed to grow super-linearly. The strong rate of convergence (in $\mathcal{L}^2$-sense) is shown to be arbitrarily close to one which is consistent with the corresponding result on the classical Milstein scheme obtained for coefficients satisfying global Lipschitz conditions.

Citation: Chaman Kumar. On Milstein-type scheme for SDE driven by Lévy noise with super-linear coefficients. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1405-1446. doi: 10.3934/dcdsb.2020167
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