Limit theorems for an inverse Markovian Hawkes process.

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history. We consider an inverse Markovian Hawkes process which combines features of several existing models of self-exciting processes and has been widely applied in insurance, finance, queue theory, statistic, and many other fields. We study the limit theorems for an inverse Markovian Hawkes process. In particular, we obtain central limit theorems and law of large numbers with several key results. [ABSTRACT FROM AUTHOR]