Study on stochastic models of population genetics by means of the theories of stochastic processes

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Stochastic models of population genetics were studied by means of the theories of stochastic processes. First, several models with the fluctuation of population size were investigated and the relation between these models was disclosed. Next, some properties of the multi-dimensional stochastic models with compensatory fitness interaction were studied. Further, two results were obtained for a stochastic model described by a birth and death process. The first result was properties of the conditional process conditional on hitting the specified boundary point prior to the other boundary point. The second was some limit theorems of this stochastic model under weak mutation.