Modelling and Simulation by Stochastic Interacting Particle Systems

Summary

Stochastic interacting particle systems (IPSs) are individual-based models, which include stochastic local interactions on a spatial lattice. In this respect an IPS works similarly to a cellular automaton. However, IPSs are continuous-time Markov processes, hence there is a large background of analytical methods. Further, one has the possibility to simulate the system on a finite lattice, which is what we focus on in this work. We explain the modelling steps broadly and by means of examples. Finally, we state the core of a simulation algorithm. The ideas is to convince the reader that IPSs can be used to set up and simulate sophisticated and applicable models but allow an analytical approach as well.