Geodesic
On integral of a semi-Markov diffusion process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 276-291 Cet article a éte moissonné depuis la source Math-Net.Ru

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A semi-Markov diffusion process $(X(t))$ $(t\ge0)$ is considered. The process $(J(t))$ $(t\ge0)$ equals to integral of the process $(X(t))$ on interval $[0,T)$ is studied. The relation between one-dimensional differential equation of the second order of elliptical type and asymptotics of a solution of Dirichlet problem on an interval with length tending to zero is derived. This relation is used for deriving a differential equation Laplace transform for the semi-Markov generating function of the process $(J(t))$. 
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     title = {On integral of {a~semi-Markov} diffusion process},
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B. P. Harlamov. On integral of a semi-Markov diffusion process. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 276-291. http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a17/

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