Nonparametric estimation of the stationary density for Hawkes-diffusion
systems with known and unknown intensity
Nonparametric estimation of the stationary density for Hawkes-diffusion
systems with known and unknown intensity
We investigate the nonparametric estimation problem of the density $\pi$, representing the stationary distribution of a two-dimensional system $\left(Z_t\right)_{t \in[0, T]}=\left(X_t, \lambda_t\right)_{t \in[0, T]}$. In this system, $X$ is a Hawkes-diffusion process, and $\lambda$ denotes the stochastic intensity of the Hawkes process driving the jumps of $X$. Based on the …