Parameter estimation for fractional power type diffusion: A hybrid Bayesian-deep learning approach

Abstract.: In this article, we consider the problem of parameter estimation in a power-type diffusion driven by fractional Brownian motion with Hurst parameter in (Formula presented.). To estimate the parameters of the process, we use an approximate bayesian computation method. Also, a particular case is addressed by means of variations and wavelet-type methods. Several theoretical properties of the process are studied and numerical examples are provided in order to show the small sample behavior of the proposed methods.