Diffusion Approximation of Branching Processes in Semi-Markov Environment

Nikolaos Limnios () and Elena Yarovaya
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Nikolaos Limnios: Sorbonne University Alliance
Elena Yarovaya: Lomonosov Moscow State University

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 4, 1583-1590

Abstract: Abstract We consider continuous-time Markov branching processes in semi-Markov random environment and obtain diffusion approximation results for the near critical case. The problem of semi-Markov environment, presented here, is new and more interesting than the Markov case, since it includes many particular interesting cases: Markov, renewal, etc. The particular case of the Markov random environment of continuous-time branching process diffusion approximation results are obtained.

Keywords: Branching process; Semi-Markov environment; Diffusion approximation; Near critical case; Random environment; 60J80; 60K15; 60K37; 60J60 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-020-09814-w

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