SECOND-ORDER ASYMPTOTIC EXPANSION FOR THE DISTRIBUTION OF PARTICLES IN A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

Zhiqiang Gao (1) , Quansheng Liu (2)

1 SMS - School of Mathematical Sciences [Beijing]
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We consider a branching random walk in which offspring distribution and moving laws both depend on an independent and identically distributed environment indexed by the time. For A ⊂ R , let Z n (A) be the number of particles of generation n located in A. We give the second-order asymptotic expansion for the counting measure Z n (·) with appropriate normalization.

Mots clés: central limit theorem; branching random walks; random envrionment; asymptotic expansion

Domaines: Probabilités [math.PR]

Zhiqiang Gao, Quansheng Liu. SECOND-ORDER ASYMPTOTIC EXPANSION FOR THE DISTRIBUTION OF PARTICLES IN A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME. 2015. ⟨hal-01244736v1⟩