LAN property for families of distributions of solutions to Levy driven SDE's

TL;DR

This paper establishes the Local Asymptotic Normality (LAN) property for statistical models based on discrete observations of solutions to Levy-driven SDEs, using Malliavin calculus techniques.

Contribution

It introduces a general sufficient condition for LAN in models based on discrete Markov process observations, specifically applied to Levy-driven SDEs.

Findings

Proves LAN property for Levy-driven SDE solutions

Develops a Malliavin calculus-based approach for derivatives of log-likelihood

Provides a framework for statistical inference in Levy-driven SDE models

Abstract

The LAN property is proved in the statistical model based on discrete-time observations of a solution to a L\'{e}vy driven SDE. The proof is based on a general sufficient condition for a statistical model based on a 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.