In this project, we will first look into the concepts of time-changing of diffusion processes, unbiased density estimation and Malliavin calculus, and then proceed to error analysis. The unbiased estimation method we examine invites infinite variance, so we aim to develop error analysis of a perturbed version of the unbiased method (that is, biased with a finite estimator variance) for multivariate time-changed diffusion processes. We may also investigate how the perturbation affects the singularity of the original density function, such as nondifferentiable cusps.
The University of Sydney
Kenneth Guo is a third-year undergraduate student in the University of Sydney. His research focus lies somewhere on the amorphous boundary between applied (financial) mathematics and statistics, with interests in modelling the real world and also estimating certain densities. He has most recently been investigating errors of a multidimensional density estimator.