Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes

We develop a quasi-likelihood analysis procedure for general class of multivariate marked point processes. As by-product the method, we establish under stability and ergodicity conditions local asymptotic normality quasi-log likelihood, along with convergence moments quasi-Bayesian estimators. To illustrate approach, then turn our attention to Hawkes processes generalized exponential kernels, comprising among others so-called Erlang kernels. provide explicit on kernel functions mark dynamics which certain transformation original process is Markovian V-geometrically ergodic. finally prove that latter result, interest in its own right, constitutes key ingredient show falls scope application analysis.