Rumours, consensus and epidemics on networks

The Poisson process is one of the most widely used models of a continuous time stochastic process. Along with Brownian motion, it can be considered as a fundamental example of such processes. The Poisson process is a counting process Nt, t ≥ 0, (a non-decreasing integer-valued process which counts the number of ‘points’ or ‘events’ up to time t) indexed by the time parameter t, which will be positive real-valued in most of our examples.