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 Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 1, Pages 183–188 (Mi tvp3526)

Short Communications

A note on diffusion-type approximation to branching processes in random environments

K. A. Borovkov

University of Melbourne, Department of Mathematics and Statistics

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.

DOI: https://doi.org/10.4213/tvp3526

Full text: PDF file (709 kB)

English version:
Theory of Probability and its Applications, 2003, 47:1, 132–138

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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

Citation in format AMSBIB
\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 \mathnet{http://mi.mathnet.ru/tvp3526} \crossref{https://doi.org/10.4213/tvp3526} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1978708} \zmath{https://zbmath.org/?q=an:1039.60075} \transl \jour Theory Probab. Appl. \yr 2003 \vol 47 \issue 1 \pages 132--138 \crossref{https://doi.org/10.1137/S0040585X97979573} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000183800400012} 

• http://mi.mathnet.ru/eng/tvp3526
• https://doi.org/10.4213/tvp3526
• http://mi.mathnet.ru/eng/tvp/v47/i1/p183

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Limnios N. Yarovaya E., “Diffusion Approximation of Near Critical Branching Processes in Fixed and Random Environment”, Stoch. Models
2. Bansaye V. Simatos F., “on the Scaling Limits of Galton-Watson Processes in Varying Environments”, Electron. J. Probab., 20 (2015), 75
3. Bansaye V., Caballero M.-E., Meleard S., “Scaling Limits of Population and Evolution Processes in Random Environment”, Electron. J. Probab., 24 (2019), 19