Transition probability densities of birth and death processes with finite state space

概要

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We consider birth and death processes with finite state space consisting of N+1 points(N ≥ 2). These processes can be treated as one-dimensional generalized diffusion processes and have transition probability densities with respect to a discrete measure called the speed measure. We give explicit representations of transition probability densities according to boundary conditions. Following a general theory on elementary solutions, we obtain integral representations of transition probability densities. Through these integralrepresentations it is not easy to see, however, the effects of boundary conditions on transition probability densities. We give eigen function expansions of transition probability　densities to see how boundary conditions affect transition probability densities.
奈良女子大学の論文
2010-03-31