Details

Autor(en) / Beteiligte

• Vatutin, V. A.
• Smadi, C.

Titel

Critical Branching Processes in a Random Environment with Immigration: The Size of the Only Surviving Family

Ist Teil von

• Proceedings of the Steklov Institute of Mathematics, 2022-03, Vol.316 (1), p.336-355

Ort / Verlag

Moscow: Pleiades Publishing

Erscheinungsjahr

2022

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We consider a critical branching process in an i.i.d. random environment in which one immigrant arrives at each generation. Let be the event that all individuals alive at time are offspring of the immigrant which joined the population at time . We study the conditional distribution of given when is large and follows different asymptotics which may be related to ( fixed, close to , or going to infinity but far from ).