JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.331, pp.196-207, 2018 (Journal Indexed in SCI)
Article / Article
Title of Journal :
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Optimal control, Runge-Kutta method, Stochastic differential equation, Stratonovich-Taylor expansion, Numerical solution, Minimal truncation error, DIFFERENTIAL-EQUATIONS, ORDER CONDITIONS, APPROXIMATION
In this work, we obtain strong order-1 conditions with minimal truncation error constants of Runge-Kutta method for the optimal control of stochastic differential equations (SDEs). We match Stratonovich-Taylor expansion of the exact solution with Stratonovich-Taylor expansion of our approximation method that is defined by the Runge-Kutta scheme, term by term, in order to get the strong order-1 conditions. By a conclusion and an outlook to future research, the paper ends. (C) 2017 Elsevier B.V. All rights reserved.