Palm versions of Hawkes processes

Abstract

This brief paper identifies the Palm distribution of a linear Hawkes process. The textbook example for Palm distributions is the Palm version of a stationary Poisson process that corresponds to the original process plus a point in zero. The present result generalizes this example in a more complex but nevertheless tractable way. As a next step, we derive the intensity measure of the Palm version of a Hawkes process and show how it could be used for estimation. Finally, we discuss further possible applications to the theory of Hawkes processes