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Dr. Mariano Rodrigo's Talk
Time: November 11th, 2025, 11:30 AM - 12:30 PM
Location: Talbot College 203 (TC 203)
Speaker: Dr. Mariano Rodrigo - Associate Professor - School of Mathematics and Applied Statistics, University of Wollongong, Australia
Title: Bridging exact and approximate solutions to Itô stochastic differential equations: a recursive series approach
Abstract: This talk presents a unified framework for deriving exact and approximate analytical solutions to Itô stochastic differential equations (SDEs). By associating each SDE with a linear first-order partial differential equation of a constructed operator, we develop a recursive series converging under a verifiable condition. Classical closed-form solutions for linear models emerge as special cases, while exact solutions are obtained for nonlinear SDEs, including stochastic logistic and Gompertz models. When closed forms are unavailable, truncated series provide practical implicit approximations validated by numerical simulations. The method accommodates time-dependent coefficients and nonlinearities, offering a flexible tool for stochastic modelling in finance, biology and engineering.