Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 131–149 | Cite as

Moments of general time dependent branching processes with applications

  • T. F. MóriEmail author
  • S. Rokob


We give sufficient conditions for a Crump–Mode–Jagers process to be bounded in Lk for a given k > 1. This result is then applied to a recent random graph process motivated by pairwise collaborations and driven by time-dependent branching dynamics. We show that the maximal degree has the same rate of increase as the degree process of a fixed vertex.

Key words and phrases

Crump–Mode–Jagers process Burkholder–Rosenthal nequality renewal equation evolving random graph maximal degree 

Mathematics Subject Classification

05C80 60F25 60J85 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Probability Theory and StatisticsEötvös Loránd UniversityBudapestHungary
  2. 2.Department of StochasticsBudapest University of Technology and EconomicsBudapestHungary

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