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Convergence in Lp and its exponential rate for a branching process in a random environment


 
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1. Title Title of document Convergence in Lp and its exponential rate for a branching process in a random environment
 
2. Creator Author's name, affiliation, country Chunmao Huang; Harbin Institute of Technology at Weihai; China
 
2. Creator Author's name, affiliation, country Quansheng Liu; University Bretagne -Sud; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) branching process, varying environment, random environment, moments, exponential convergence rate, Lp convergence
 
3. Subject Subject classification 60K37, 60J80
 
4. Description Abstract We consider a supercritical branching process $(Z_n)$ in a random environment $\xi$. Let $W$ be the limit of the normalized population size $W_n=Z_n/\mathbb{E}[Z_n|\xi]$.  We first show a necessary  and sufficient condition for the quenched $L^p$ ($p>1$) convergence of $(W_n)$, which completes the known result for the annealed $L^p$ convergence. We then show that the convergence rate is exponential, and we find  the maximal value of $\rho>1$ such that $\rho^n(W-W_n)\rightarrow 0$ in $L^p$, in both quenched and annealed sense. Similar results are also shown for a branching process in a varying environment.
 
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7. Date (YYYY-MM-DD) 2014-11-03
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3388
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3388
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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