Could anyone point me towards, articles, or any other reading material regarding ergodic theorem for Bounded Random Walks. 1) Consider an simple bounded (x,y) plane on which several 2-dimensional random walker are randomly assigned an (x,y) coordinate. 2) Furthermore, if 2 random walkers collide 1 of them dies off. I have tried time series, Markov Chains etc... But I can't seem to be able to factor in the interaction between 2 elements. http://demonstrations.wolfram.com/PredatorPreyEcosystemARealTimeAgentBasedSimulation/ I'm working on a simpler version of this simulation.