naa a22 4500 51081199X CHVBK 20180411083446.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1134/S0081543813060060 doi (NATIONALLICENCE)springer-10.1134/S0081543813060060 Bulinskaya E. Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut Subcritical catalytic branching random walk with finite or infinite variance of offspring number [Elektronische Daten] [E. Bulinskaya] 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 + δ is required where δ is some positive number. Pleiades Publishing, Ltd., 2013 Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 62-72 0081-5438 282:1<62 2013 282 11501 https://doi.org/10.1134/S0081543813060060 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813060060 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bulinskaya E. Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 62-72 0081-5438 282:1<62 2013 282 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer