Stationary Matern hard core processes of the third type.

Bertil Matern has introduced in his seminal D.Sc. thesis work from 1960 several important spatial models, including what is now known as the Matern hard core point processes of type I and II (shortly, Matern I and II).  For a given hard core parameter R and a primary Poisson process in space with constant intensity, Matern I is the secondary point process obtained by retaining every primary point which is not within distance R from another primary point. Assuming the primary process proceeds at a uniform speed in the time interval from 0 to 1, Matern II is the secondary point process obtained by retaining every primary point x which is not within distance R from another primary point which occurred prior to x. Matern, in his thesis work, briefly mentioned a third type of hard core process, where instead every primary point x is retained if no secondary point which occurred prior to x is within distance R from x. This project deals with this less well-known but more appealing or realistic hard core point process model which we refer to as the stationary Matern's hard core process of type III or shortly Matern III. In the finite case, though Matern found the model of type III too complicated for analyzis, it is in fact the only model of Matern I-III which has a tractable likleihood!
The focus in the project is on the stationary and hence infinite Matern III process from a stochastic geometric point of view.