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Central limit theorem for a critical multi-type branching process in random environment
- Publication Year :
- 2020
-
Abstract
- Let (Z n) n≥0 with Z n = (Z n (i, j)) 1≤i,j≤p be a p multi-type critical branching process in random environment, and let M n be the expectation of Z n given a fixed environment. We prove theorems on convergence in distribution of sequences of branching processes Zn |Mn| /|Z n | > 0 and ln Zn √ n /|Z n | > 0. These theorems extend similar results for single-type critical branching process in random environment.; Soit (Z n) n≥0 , avec Z n = (Z n (i, j)) 1≤i,j≤p, un processus de branchement multi-type et critique en environnement aléatoire. Soit M n la matrice moyenne de Z n à environnement fixé. Nous démontrons des théorèmes de convergence en distribution des suites (Zn/ |Mn| ) et ( Zn /√ n) conditionnellement à la non extinction (|Z n | > 0). Ces théorèmes étendent dans le cadre multi-type des résultats antérieurs connus pour des processus uni-type.
- Subjects :
- Discrete mathematics
random environments
General Mathematics
010102 general mathematics
Probability (math.PR)
central limit theorem
01 natural sciences
multi-type branching process
Branching (linguistics)
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
010104 statistics & probability
critical case
Convergence of random variables
Random environment
FOS: Mathematics
0101 mathematics
Mathematics - Probability
Central limit theorem
Mathematics
Branching process
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....35bf7e3cfd3b0c8f98df19b5cb3937ca