A0328
Title: Parameter estimation with increased precision for elliptic and hypo-elliptic diffusions
Authors: Yuga Iguchi - University College London (United Kingdom) [presenting]
Alexandros Beskos - University College London (United Kingdom)
Matthew Graham - University College London (United Kingdom)
Abstract: Parameter estimation is considered for elliptic and hypoelliptic diffusions. Established approaches for likelihood-based estimation invoke a numerical time discretisation scheme for the approximation of the generally intractable transition dynamics of the Stochastic Differential Equation (SDE) over finite time periods. First, we propose two weak second-order sampling schemes to cover both the hypoelliptic and elliptic classes and generate novel transition density schemes of the SDE, i.e., approximations of the SDE transition density. We then provide a collection of analytical and numerical results that solidifies the proposed schemes and showcases advantages from their incorporation within SDE calibration methods, under both high and low-frequency observations regime. Typically, for hypoelliptic diffusions, the proposed contrast estimator constructed from the transition density scheme achieves asymptotic normality under the weakest requirement for the step size of observations in the literature.
