Second derivative of the log-likelihood in the model given by a Levy driven stochastic differential equations

TL;DR

This paper derives an integral representation for the second derivative of the log-likelihood in Levy-driven SDE models using Malliavin calculus, aiding statistical inference for such processes.

Contribution

It introduces a novel integral representation for the second derivative of the log-likelihood in Levy-driven SDEs utilizing Malliavin calculus, enhancing analytical tools for these models.

Findings

Provides a new integral formula for second derivatives of log-likelihood

Facilitates improved statistical inference in Levy-driven SDEs

Extends Malliavin calculus techniques to complex stochastic models

Abstract

By means of the Malliavin calculus, integral representation for the second derivative of the loglikelihood function are given for a model based on discrete time observations of the solution to SDE driven by a Levy process.