Abstract:
We extend the known results on diffusion-type approximation to branching processes in random environments. In particular, the range of the initial values of the processes can be much wider, moment conditions are more general, and the approximant can be a discontinuous process. The proof is based on the author's estimates for diffusion approximation to branching processes in varying environments.
Keywords:branching process in random environments, diffusion approximation.
Citation:
K. A. Borovkov, “A note on diffusion-type approximation to branching processes in random environments”, Teor. Veroyatnost. i Primenen., 47:1 (2002), 183–188; Theory Probab. Appl., 47:1 (2003), 132–138
\Bibitem{Bor02}
\by K.~A.~Borovkov
\paper A note on diffusion-type approximation to branching processes in random environments
\jour Teor. Veroyatnost. i Primenen.
\yr 2002
\vol 47
\issue 1
\pages 183--188
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\crossref{https://doi.org/10.4213/tvp3526}
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\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 1
\pages 132--138
\crossref{https://doi.org/10.1137/S0040585X97979573}
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Linking options:
https://www.mathnet.ru/eng/tvp3526
https://doi.org/10.4213/tvp3526
https://www.mathnet.ru/eng/tvp/v47/i1/p183
This publication is cited in the following 5 articles:
Limnios N. Yarovaya E., “Diffusion Approximation of Branching Processes in Semi-Markov Environment”, Methodol. Comput. Appl. Probab., 22:4 (2020), 1583–1590
Bansaye V., Caballero M.-E., Meleard S., “Scaling Limits of Population and Evolution Processes in Random Environment”, Electron. J. Probab., 24 (2019), 19
Limnios N. Yarovaya E., “Diffusion Approximation of Near Critical Branching Processes in Fixed and Random Environment”, Stoch. Models, 35:2 (2019), 209–220
Bansaye V. Simatos F., “on the Scaling Limits of Galton-Watson Processes in Varying Environments”, Electron. J. Probab., 20 (2015), 75
Vincent Bansaye, Sylvie Méléard, Stochastic Models for Structured Populations, 2015, 39