Research about effects of boundary states on conditional distributions

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The method of harmonic transform is a useful one to analyze some properties of Green kernels and diffusion processes. It should be noted that these Green kernels and diffusion processes are minimal. However minimal stochastic processes are not always treated in applied mathematics such as population genetics. In our research, conditional distributions of non minimal generalized diffusion processes and the effect of asymptotic behavior of sample paths near the boundaries on conditional distributions are investigated.