Chapter 4: The Strong Law for a type of self-interaction; the center of mass
In this chapter our goal is to obtain a strong (a.s.) limit theorem for a spatial branching system, but with a new feature: the particles, besides moving and branching, now also interact with each other.
To this end, we introduce a branching Brownian motion (BBM) with 'attraction' or 'repulsion' between the particles.