Asymptotic expansion of a functional constructed from a semi-Markov random evolution in the scheme of diffusion approximation

Koroliouk, V.; Samoĭlenko, I.

doi:10.1090/tpms/1035

Asymptotic expansion of a functional constructed from a semi-Markov random evolution in the scheme of diffusion approximation

Authors: V. S. Koroliouk and I. V. Samoĭlenko
Translated by: N. N. Semenov
Journal: Theor. Probability and Math. Statist. 96 (2018), 83-100
MSC (2010): Primary 60J25; Secondary 35C20
DOI: https://doi.org/10.1090/tpms/1035
Published electronically: October 5, 2018
MathSciNet review: 3666873
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Abstract: The regular and singular components of an expansion of a functional of a semi-Markov decomposition of a random evolution are found in the paper. A procedure is proposed for finding the explicit form of initial conditions for $t=0$ by using the boundary conditions for the singular component of the expansion,

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