Abstract
Some efficient stochastic Runge–Kutta (SRK) methods for the strong as well as for the weak approximation of solutions of stochastic differential equations (SDEs) with improved computational complexity are considered. Their convergence is analyzed by a concise colored rooted tree approach for both, Ito as well as Stratonovich SDEs. Further, order conditions for the coefficients of order 1.0 and 1.5 strong SRK methods as well as for order 2.0 weak SRK methods are given. As the main novelty, the computational complexity of the presented order 1.0 strong SRK method and the order 2.0 weak SRK method depends only linearly on the dimension of the driving Wiener process. This is a significant improvement compared to well known methods where the computational complexity depends quadratically on the dimension of the Wiener process.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
