LAN property for discretely observed solutions to Lévy driven SDE’s

Abstract

The LAN property is proved in the statistical model based on discrete-time observations of a solution to a Lévy driven SDE. The proof is based on a general sufficient condition for a statistical model based on discrete observations of a Markov process to possess the LAN property, and involves substantially the Malliavin calculus-based integral representations for derivatives of log-likelihood of the model.

Keywords

• LAN property
• likelihood function
• Lévy driven SDE
• regular statistical experiment