No. 960

Title:

Nonparametric inference for Lévy processes by continuous observation: a martingale approach

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Nonparametric inference, Levy process, martingale, empirical process

Abstract:

    We consider a nonparametric estimation problem of the Lévy measure of time-inhomogeneous Lévy process. We derive the functional asymptotic normality and efficiency in an $ \ell ^\infty $-space. In time-homogeneous case, we propose a goodness-of-fit test which is asymptotically distribution free. Our result is a fruit of the empirical process theory and the martingale theory.