BERRY -ESSEEN BOUND AND CRAMÉR MODERATE DEVIATION EXPANSION FOR A SUPERCRITICAL BRANCHING RANDOM WALK

Thi Thuy Bui (1) , Ion Grama (1) , Quansheng Liu (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We consider a supercritical branching random walk where each particle gives birth to a random number of particles of the next generation, which move on the real line, according to a fixed law. Let $Z_ n$ be the counting measure which counts the number of particles of nth generation situated in a given region. Under suitable conditions, we establish a Berry-Esseen bound and a Cramér type moderate deviation expansion for $Z_n$ with suitable norming.

Domaines: Probabilités [math.PR]

Thi Thuy Bui, Ion Grama, Quansheng Liu. BERRY -ESSEEN BOUND AND CRAMÉR MODERATE DEVIATION EXPANSION FOR A SUPERCRITICAL BRANCHING RANDOM WALK. 2020. ⟨hal-02933786⟩