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 Tr. Mat. Inst. Steklova, 2013, Volume 282, Pages 69–79 (Mi tm3490)

Subcritical catalytic branching random walk with finite or infinite variance of offspring number

E. Vl. Bulinskaya

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: Subcritical catalytic branching random walk on the $d$-dimensional integer lattice is studied. New theorems concerning the asymptotic behavior of distributions of local particle numbers are established. To prove the results, different approaches are used, including the connection between fractional moments of random variables and fractional derivatives of their Laplace transforms. In the previous papers on this subject only supercritical and critical regimes were investigated under the assumptions of finiteness of the first moment of offspring number and finiteness of the variance of offspring number, respectively. In the present paper, for the offspring number in the subcritical regime, the finiteness of the moment of order $1+\delta$ is required where $\delta$ is some positive number.

DOI: https://doi.org/10.1134/S0371968513030060

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English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 282, 62–72

Bibliographic databases:

UDC: 519.218.25

Citation: E. Vl. Bulinskaya, “Subcritical catalytic branching random walk with finite or infinite variance of offspring number”, Branching processes, random walks, and related problems, Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences, Tr. Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 69–79; Proc. Steklov Inst. Math., 282 (2013), 62–72

Citation in format AMSBIB
\Bibitem{Bul13} \by E.~Vl.~Bulinskaya \paper Subcritical catalytic branching random walk with finite or infinite variance of offspring number \inbook Branching processes, random walks, and related problems \bookinfo Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences \serial Tr. Mat. Inst. Steklova \yr 2013 \vol 282 \pages 69--79 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3490} \crossref{https://doi.org/10.1134/S0371968513030060} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3308582} \elib{http://elibrary.ru/item.asp?id=20280546} \transl \jour Proc. Steklov Inst. Math. \yr 2013 \vol 282 \pages 62--72 \crossref{https://doi.org/10.1134/S0081543813060060} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000325961800006} \elib{http://elibrary.ru/item.asp?id=21883299} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84885984473} 

• http://mi.mathnet.ru/eng/tm3490
• https://doi.org/10.1134/S0371968513030060
• http://mi.mathnet.ru/eng/tm/v282/p69

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This publication is cited in the following articles:
1. E. Vl. Bulinskaya, “Complete classification of catalytic branching processes”, Theory Probab. Appl., 59:4 (2015), 545–566
2. E. V. Bulinskaya, “Spread of a catalytic branching random walk on a multidimensional lattice”, Stoch. Process. Their Appl., 128:7 (2018), 2325–2340
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