  Due to its clustering and self-exciting properties, the Hawkes process has
been used extensively in numerous fields ranging from sismology to finance.
Since data is often aquired on regular time intervals, we propose a piece-wise
constant model based on a Discrete-Time Hawkes Process (DTHP). We prove that
this discrete-time model converges to the usual continuous-time Hawkes process
as the time-step tends to zero.
