For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions.
Lina JI
,
Xiangqi ZHENG
. MOMENTS OF CONTINUOUS-STATE BRANCHING PROCESSES IN LÉVY RANDOM ENVIRONMENTS[J]. Acta mathematica scientia, Series B, 2019
, 39(3)
: 781
-796
.
DOI: 10.1007/s10473-019-0310-7
[1] Luschgy H, Pagès G. Moment estimates for Lévy processes. Electron Commun Prob, 2008, 13:422-434
[2] Li Z. Measure-Valued Branching Markov Processes. Heidelberg:Springer-Verlag, 2011
[3] Gün O, König W, Sekulovió O. Moment asymptotics for branching random walks in random environment. Electron J Probab, 2013, 18(63):1-18
[4] Agarwal R, Hristova S, Kopanov P, O'regan D. Impulsive differential equations with Gamma distributed moments of impulses and p-moment exponential stability. Acta Mathematica Scientia, 2017, 37B(4):985- 997
[5] Qiu D, Chen P, Andrei V. Complete moment convergence for LP-mixingales. Acta Mathematica Scientia, 2017, 37B(5):1319-1330
[6] Zhao Y. Asymptotic properties of the moment convergence for NA sequences. Acta Mathematica Scientia, 2014, 34B(2):301-312
[7] Barczy M, Li Z, Pap G. Moment formulas for multitype continuous state and continuous time branching process with immigration. J Theor Probab, 2016, 29(3):958-995
[8] Ji L, Li Z. Moments of continuous-state branching processes with or without immigration. 2017[2018-03-31]. https://arxiv.org/abs/1702.08698
[9] Jiřina M. Stochastic branching processes with continuous state space. Czech Math J, 1958, 8:292-313
[10] Bansaye V, Millan J C P, Smadi C. On the extinction of continuous state branching processes with catastrophes. Electron J Probab, 2013, 18(106):1-31
[11] Palau S, Pardo J C. Continuous state branching processes in random environment:the Brownian case. Stoch Process Appl, 2017, 127:957-994
[12] He H, Li Z, Xu W. Continuous-state branching processes in Lévy random environments. J Theor Probab, 2017[2018-03-31]. https://doi.org/10.1007/s10959-017-0765-1
[13] Palau S, Pardo J C. Branching processes in a Lévy random environment. Acta Appl Math, 2018, 153(1):55-79
[14] Dawson D A, Li Z. Stochastic equations, flows and measure-valued processes. Ann Probab, 2012, 40(2):813-857
[15] Caballero M E, Lambert A, Uribe Bravo G. Proof(s) of the Lamperti representation of continuous-state branching processes. Probab Surv, 2009, 6:62-89
[16] Sato K I. Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, 1999
[17] Athreya K B, Ney P E. Branching Processes. Berlin:Springer, 1972