Explicit Expansions for Multivariate Diffusions

Abstract

In this paper, by adopting a quasi-Lamperti transform unitizing the process’ diffusion matrix at the initial time, we provide a new explicit recursive formula to compute the expansion coefficients for the pathwise Taylor expansion method of Li (2013). The quasi-Lamperti transform also allows us to recalculate the expansion coefficients for the Hermite expansion method of Wan and Yang (2020) via the pathwise Taylor expansion method, and proves the equivalence between the methods of Li (2013) and Wan and Yang (2020). Based on the established connection between the delta expansion method of Yang et al. (2019) and the Hermite expansion method of Wan and Yang (2020), we unifies the three expansion methods.