A0263
Title: Analytical approximations for diffusion processes with asymptotic expansion
Authors: Emanuele Guidotti - University of Lugano (Switzerland) [presenting]
Nakahiro Yoshida - University of Tokyo (Japan)
Abstract: A comprehensive framework is presented for constructing analytical approximations of functionals of diffusion processes using asymptotic expansions in small noise regimes. Building on the Malliavin calculus, high-order expansions are derived for the probability density function, cumulative distribution function, characteristic function, moments, and quantile function of general diffusion processes. The method systematically develops these expansions for joint, marginal, and conditional distributions. A formal computational scheme is proposed to compute expansion formulas of arbitrary order. This approach allows accurate approximations in models where direct analytical solutions are unavailable, and it is broadly applicable to problems in mathematical finance, filtering, and inference for stochastic systems.
