Before revision:  We discuss the estimation error and provide some numerical examples . Applications to high frequency trading events in financial markets and to earthquakes occurrence dynamics are  considered.
After revision:  In this paper, we perform a systematic study of this non-parametric estimation procedure in the general framework of marked Hawkes processes. We describe precisely this procedure step by step. We discuss the estimation error and provide some numerical examples . Applications to high frequency trading events in financial markets and to earthquakes occurrence dynamics are considered.