A New Explicit Magnus Expansion for Nonlinear Stochastic Differential Equations

Xiaoling Wang, Xiaofei Guan and Pei Yin
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Xiaoling Wang: Department of Mathematics,Tianjin Chengjian University, Tianjin 300384, China
Xiaofei Guan: Department of Mathematics, Tongji University, Shanghai 200092, China
Pei Yin: Business School, University of Shanghai for Science and Technology, Shanghai 200092, China

Mathematics, 2020, vol. 8, issue 2, 1-17

Abstract: In this paper, based on the iterative technique, a new explicit Magnus expansion is proposed for the nonlinear stochastic equation d y = A ( t , y ) y d t + B ( t , y ) y ? d W . One of the most important features of the explicit Magnus method is that it can preserve the positivity of the solution for the above stochastic differential equation. We study the explicit Magnus method in which the drift term only satisfies the one-sided Lipschitz condition, and discuss the numerical truncated algorithms. Numerical simulation results are also given to support the theoretical predictions.

Keywords: explicit Magnus expansion; asymptotic stability; Stratonovich integral; Itô integral; nonlinear stochastic equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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