摘要
We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoting the counting measure of particles of generation n, and Eξ the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-degenerate.
We consider a branching random walk in an independent and identically distributed random environment ξ=（ξn） indexed by the time.Let W be the limit of the martingale Wn=∫e-txZn（dx）/Eξ∫e-txZn（dx）,with Zn denoting the counting measure of particles of generation n,and Eξ the conditional expectation given the environment ξ.We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W,when W is non-degenerate.
作者
Yuejiao WANG
Zaiming LIU
Quansheng LIU
Yingqiu LI
王月娇;刘再明;刘全升;李应求(College of Mathematics and Computational Science, Hunan First Normal University, Changsha 410205, China;School of Mathematics and Statistics, Central South University, Changsha 410083, China;LMBA, UMR CNRS 6205, Université de Bretagne-Sud, F-56000 Vannes, France;School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410004, China)
基金
benefited from the support of the French government Investissements d’Avenir program ANR-11-LABX-0020-01
partially supported by the National Natural Science Foundation of China(11571052,11401590,11731012 and 11671404)
by Hunan Natural Science Foundation(2017JJ2271)
