naa a22 4500 510812031 CHVBK 20180411083447.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1134/S0081543813060035 doi (NATIONALLICENCE)springer-10.1134/S0081543813060035 Lower large deviations for supercritical branching processes in random environment [Elektronische Daten] [Vincent Bansaye, Christian Böinghoff] Branching processes in random environment (Z n : n ≥ 0) are the generalization of Galton-Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. In the supercritical regime, the process survives with a positive probability and grows exponentially on the non-extinction event. We focus on rare events when the process takes positive values but lower than expected. More precisely, we are interested in the lower large deviations of Z, which means the asymptotic behavior of the probability {1 ≤ Z n ≤ exp(nθ)} as n → ∞. We provide an expression for the rate of decrease of this probability under some moment assumptions, which yields the rate function. With this result we generalize the lower large deviation theorem of Bansaye and Berestycki (2009) by considering processes where ℙ(Z 1 = 0 | Z 0 = 1) > 0 and also much weaker moment assumptions. Pleiades Publishing, Ltd., 2013 Bansaye Vincent École Polytechnique, 91128, Palaiseau Cedex, France aut Böinghoff Christian Fachbereich Mathematik, Goethe-Universität, Fach 187, D-60054, Frankfurt am Main, Germany aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 15-34 0081-5438 282:1<15 2013 282 11501 https://doi.org/10.1134/S0081543813060035 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813060035 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bansaye Vincent École Polytechnique, 91128, Palaiseau Cedex, France aut NATIONALLICENCE 700 1- Böinghoff Christian Fachbereich Mathematik, Goethe-Universität, Fach 187, D-60054, Frankfurt am Main, Germany aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 15-34 0081-5438 282:1<15 2013 282 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer