Continuous Time Branching Random Walk

What is in this chapter? Branching random walks are among the simplest continuous time spatial processes. Consider a system of particles that undergo branching and random motion on a countable graph (such as Zd or a homogeneous tree) according to the two following rules. A particle at x waits an exponential random time with rate λp(x, y) > 0 and then gives birth to a particle at y. p(x, y) are the transition probabilities of a Markov chain and λ > 0 is a parameter. A particle waits an exponential time with rate 1 and then dies.