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A New Explicit Magnus Expansion for Nonlinear Stochastic Differential Equations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xiaoling Wang & Xiaofei Guan & Pei Yin, 2020. "A New Explicit Magnus Expansion for Nonlinear Stochastic Differential Equations," Mathematics, MDPI, vol. 8(2), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:183-:d:315794
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    References listed on IDEAS

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    1. G. N. Milstein & Eckhard Platen & H. Schurz, 1998. "Balanced Implicit Methods for Stiff Stochastic Systems," Published Paper Series 1998-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    2. Kahl Christian & Schurz Henri, 2006. "Balanced Milstein Methods for Ordinary SDEs," Monte Carlo Methods and Applications, De Gruyter, vol. 12(2), pages 143-170, April.
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