Geodesic
Transition functions of a~continuous semi-Markov process on the line
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VIII, Tome 130 (1983), pp. 190-205

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Necessary conditions for semi-Markov transition function of continuous process on the line to be represented as a solution of a second order differential equation are investigated. 
@article{ZNSL_1983_130_a20,
     author = {B. P. Harlamov},
     title = {Transition functions of a~continuous {semi-Markov} process on the line},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {190--205},
     publisher = {mathdoc},
     volume = {130},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_130_a20/}
}
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B. P. Harlamov. Transition functions of a~continuous semi-Markov process on the line. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VIII, Tome 130 (1983), pp. 190-205. http://geodesic.mathdoc.fr/item/ZNSL_1983_130_a20/