Calculating the Malliavin derivative of one stochastic mechanics problem

• Main Author: Lyu, Xingyu
• Other Authors: Nicolas Privault
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2019
• Subjects: Science; Science::Mathematics::Probability theory
• Online Access: https://hdl.handle.net/10356/136481
• Institution: Nanyang Technological University

The Malliavin weight sampling method is a way to tracking the dynamics of a stochastic system. In this FYP, we aim to apply this MWS method to a specific stochastic problem. First, we construct a Malliavin weight in a rigorous and precise mathematical way. Then we apply this MWS to Kelvin-Voigt stochastic model with Gaussian random variable to study the dynamic of the system with respect to some parameter in the system. We found that the dynamic of the system can be approximated by MWS method perfectly when time is close to zero and the Malliavin weight deviates from the analytical solution when time becomes larger. Then we verified this result by a numerical approximation by Euler’s explicit finite difference method. This FYP is a supplementary work for existing study on Malliavin sampling method regarding the dynamic of the Malliavin weight, especially in Kelvin-Voigt model.