Poisson cluster processes are one of the most important classes of point process models (see Daley and Vere-Jones[7] and Møller; Waagepetersen[24]). They are natural models for the location of objects in the space, and are widely used in point process studies whether theoretical or applied. Very popular and versatile Poisson cluster processes are the so-called self-exciting or Hawkes processes ...

This paper contains a completely formal (and mechanically proved) development of some algorithms dealing with a linked list supposed to be shared by various processes. These algorithms are executed in a highly concurrent fashion by an unknown number of such independent processes. These algorithms have been first presented in [MS96] by M.M. Michael and M.L. Scott. Two other developments of the s...