Séminaire du pôle Probabilités

Nonparametric Estimation for Hawkes Diffusion Systems

In this work, we study a diffusion process with jumps driven by a Hawkes process, where the intensity follows a piecewise deterministic Markov process. We begin by exploring the probabilistic properties of the system. Next, we focus on the nonparametric estimation of the coefficients in the associated stochastic differential equation (SDE), based on the minimization of various empirical contrast functions. In addition, we propose a kernel density estimation method to estimate the invariant density of the joint process formed by the diffusion component and the intensity process.
This step is essential due to the potential applications of the model. Our results are compared to those obtained for the estimation of the invariant density of a Lévy process.