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

Chaman Kumar

doi:10.3934/dcdsb.2020167

Article Contents

2021, Volume 26, Issue 3: 1405-1446. Doi: 10.3934/dcdsb.2020167

This issue Previous Article Dynamics of the QR-flow for upper Hessenberg real matrices Next Article Approximation methods for the distributed order calculus using the convolution quadrature

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

Chaman Kumar^,

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

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

Received: June 30, 2019

Revised: November 30, 2019

Early access: May 2020

Published: March 2021

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 60H10; Secondary: 60H35, 60H15.

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References

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