A0303
Title: Optimal control for parameter estimation in partially observed hypoelliptic stochastic differential equations
Authors: Quentin Clairon - ISPED - Universite de Bordeaux (France) [presenting]
Adeline Leclercq-Samson - LJK universite Joseph Fourier (France)
Abstract: The problem of parameter estimation in stochastic differential equations (SDEs) in a partially observed framework is considered. We aim to design a method working for both elliptic and hypoelliptic SDEs, the latter being characterized by degenerate diffusion coefficients. This feature often causes the failure of a contrast estimator based on the Euler Maruyama discretization scheme and dramatically impairs classic stochastic filtering methods used to reconstruct the unobserved states. All of these issues make the estimation problem in hypoelliptic SDEs difficult to solve. To overcome this, we construct a well-defined cost function no matter the elliptic nature of the SDEs. We also bypass the filtering step by considering a control theory perspective. The unobserved states are estimated by solving deterministic optimal control problems using numerical methods which do not need strong assumptions on the diffusion coefficient conditioning. Numerical simulations made on different partially observed hypoelliptic SDEs reveal our method produces accurate estimates while dramatically reducing the computational price compared to other methods.
