The Wright-Fisher equation, which was introduced as a model to study demography in the presence of diffusion, has had a renaissance as a model for the migration of alleles in the genome. Our goal in this paper is to give a careful analysis of the fundamental solution to the Wright-Fisher equation, with particular emphasis on its behavior for a short time near the boundary.

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Bisimulation is a concept that captures behavioural equivalence. It has been studied extensively on nonprobabilistic systems and on discrete-time Markov processes and on so-called continuous-time Markov chains. In the latter time is continuous but the evolution still proceeds in jumps. We propose two definitions of bisimulation on continuoustime stochastic processes where the evolution is a flow through time. We show that they are equivalent and we show that when restricted to discrete-time, our concept of bisimulation encompasses the standard discrete-time concept. The concept we introduce is not a straightforward generalization of discrete-time concepts.

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