The validity of the Edgeworth expansion for densities of linear statistics of linear processes is proved. In contrast with previous works on Edgeworth expansions for dependent processes, this result is valid under long-range dependence.

In this paper, we prove the validity of the Edgeworth expansion of the Discrete Fourier transforms of some linear time series. This result is applied to approach moments of non-linear functionals of the periodogram. As an illustration, we give an expression of the mean square error of the...

We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with respect to boundary conditions on a multidimensional...

We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with respect to boundary conditions on a multidimensional...