A1329
Title: Parameter inference for hypo-elliptic diffusions under a weak design condition
Authors: Yuga Iguchi - University College London (United Kingdom) [presenting]
Alexandros Beskos - University College London (United Kingdom)
Abstract: The problem of parameter estimation is addressed for degenerate diffusion processes defined via the solution of stochastic differential equations (SDEs) with a diffusion matrix that is not full-rank. For this class of hypo-elliptic diffusions, recent works have proposed contrast estimators that are asymptotically normal, provided that the step-size in-between observations $\Delta = \Delta_n$ and their total number n satisfying the classical high-frequency setting with $\Delta = o(n^{-1/2})$. This latter restriction requires a so-called rapidly increasing experimental design. This limitation is overcome, and a general contrast estimator is developed, satisfying asymptotic normality under the weaker design condition $\Delta = o(n^{-p/2})$ for general integer p greater than 2. Such a result has been obtained for elliptic SDEs in the literature, but its derivation in a hypo-elliptic setting is highly non-trivial. Numerical results are provided to illustrate the advantages of the developed theory.
