Fluctuations for mean-field interacting age-dependent Hawkes processes

Fluctuations for mean-field interacting age-dependent Hawkes processes

The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +∞) being granted by the study performed in [9], the aim of the present paper is to prove the resulting functional central limit theorem. It involves the study of a measure-valued process describing the fluctuations (at scale n) of the em...

Mean-field inference of Hawkes point processes

We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d-dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the fluctuations of the stochastic intensity are small. We show that this is notably the case in situations when interactions are sufficiently weak, when the dimension of t...

Mean field limit for interacting particles

Isotonic Hawkes Processes

0 g⇤(w⇤ ·xt)dt = P j2Si aijg ⇤ (w⇤ ·xj). Set y⇤ i = g ⇤ (w⇤ ·xi) to be the expected value of each yi. Let ̄ Ni be the expected value of Ni. Then we have ̄ Ni = P j2Si aijy ⇤ j . Clearly we do not have access to ̄ Ni. However, consider a hypothetical call to the algorithm with input {(xi, ̄ Ni)}i=1 and suppose it returns ḡk. In this case, we define ȳk i = ḡk(w̄k · xi). Next we begin the proof and int...

Hawkes processes in finance

In this paper we propose an overview of the recent academic literature devoted to the applications of Hawkes processes in finance. Hawkes processes constitute a particular class of multivariate point processes that has become very popular in empirical high frequency finance this last decade. After a reminder of the main definitions and properties that characterize Hawkes processes, we review th...