On Tamed Milstein Schemes of SDEs Driven by Lévy Noise

Chaman Kumar; Sotirios Sabanis

On Tamed Milstein Schemes of SDEs Driven by Lévy Noise

Chaman Kumar
, Sotirios Sabanis

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We extend the taming techniques developed in [3, 19] to construct explicit Milstein schemes that numerically approximate Lévy driven stochastic differential equations with super-linearly growing drift coefficients. The classical rate of convergence is recovered when the first derivative of the drift coefficient satisfies a polynomial Lipschitz condition.

Original language	English
Pages (from-to)	421-463
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	22
Issue number	2
Early online date	Dec 2016
Publication status	Published - Mar 2017

Keywords / Materials (for Non-textual outputs)

math.PR
Primary 60H35, secondary 65C30

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Tamed_Milstein_ArXiv_23Dec2015
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series B following peer review. The definitive publisher-authenticated version [insert complete citation information here] is available online at: https://aimsciences.org/journals/home.jsp?journalID=2
Accepted author manuscript, 297 KBLicence: Creative Commons: Attribution-NonCommercial-ShareAlike (CC BY-NC-SA)

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title = "On Tamed Milstein Schemes of SDEs Driven by L{\'e}vy Noise",

abstract = "We extend the taming techniques developed in [3, 19] to construct explicit Milstein schemes that numerically approximate L{\'e}vy driven stochastic differential equations with super-linearly growing drift coefficients. The classical rate of convergence is recovered when the first derivative of the drift coefficient satisfies a polynomial Lipschitz condition.",

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AB - We extend the taming techniques developed in [3, 19] to construct explicit Milstein schemes that numerically approximate Lévy driven stochastic differential equations with super-linearly growing drift coefficients. The classical rate of convergence is recovered when the first derivative of the drift coefficient satisfies a polynomial Lipschitz condition.

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KW - Primary 60H35, secondary 65C30

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JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

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On Tamed Milstein Schemes of SDEs Driven by Lévy Noise

Abstract

Keywords / Materials (for Non-textual outputs)

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