Modelling and Simulation by Stochastic Interacting Particle Systems
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.
KeywordsTransition Rate Cellular Automaton Cellular Automaton Range Condition Stochastic Matrix
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