A New Explicit Magnus Expansion for Nonlinear Stochastic Differential Equations

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.