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Numerical Algorithms

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30-03-2021 | Original Paper

A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations

Authors: Guoguo Yang, Kevin Burrage, Yoshio Komori, Pamela Burrage, Xiaohua Ding

Published in: Numerical Algorithms | Issue 4/2021

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Abstract

In this paper, a class of new Magnus-type methods is proposed for non-commutative Itô stochastic differential equations (SDEs) with semi-linear drift term and semi-linear diffusion terms, based on Magnus expansion for non-commutative linear SDEs. We construct a Magnus-type Euler method, a Magnus-type Milstein method and a Magnus-type Derivative-free method, and give the mean-square convergence analysis of these methods. Numerical tests are carried out to present the efficiency of the proposed methods compared with the corresponding underlying methods and the specific performance of the simulation Itô integral algorithms is investigated.

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Title: A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations
Authors: Guoguo Yang
Kevin Burrage
Yoshio Komori
Pamela Burrage
Xiaohua Ding
Publication date: 30-03-2021
Publisher: Springer US
Published in: Numerical Algorithms / Issue 4/2021
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-021-01089-7

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