On the approximation of Markov chains to determine the probability of extinction of a genotype

As it is known a precise definition of the Brownian motion involves a measure on the path space, such that it is possible to put the Brownian motion on a firm mathematical foundation. In this paper we refer to an application of asymptotic theory of stochastic differential equations in mathematical genetics. The construction of the Brownian motion as a limit of a rescaled random walk can be generalized to a class of Markov chains.