Large Deviations for Hawkes Processes with Randomized Baseline Intensity

The Hawkes process, which is generally defined for the continuous-time setting, can be described as a self-exciting simple point process with clustering effect, whose jump rate depends on its entire history. Due to past events determining future developments of processes, model not Markovian. In certain special circumstances, it Markovian generator if exciting function an exponential or sum functions. case non-Markovian difficulties arise when intensity given by baseline and other terms that depend history compared standard Poisson process. It one main methods used studying dynamical properties general highly important credit risk studies. intensity, instrumental in model, usually deterministic cases. this paper, we consider linear where randomly defined, investigate asymptotic results large deviations principle newly model. processes randomized dealt have wide applications insurance, finance, queue theory, statistics.