Estimation of subcritical Galton Watson processes with correlated immigration

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY Stochastic Processes and their Applications Pub Date : 2025-02-27 DOI:10.1016/j.spa.2025.104614

Yacouba Boubacar Maïnassara , Landy Rabehasaina

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引用次数: 0

Abstract

We consider an observed subcritical Galton Watson process

{Y_{n}, n \in Z}

with correlated stationary immigration process

{ϵ_{n}, n \in Z}

. Two situations are presented. The first one is when

Cov (ϵ_{0}, ϵ_{k}) = 0

for

k

larger than some

k_{0}

: a consistent estimator for the reproduction and mean immigration rates is given, and a central limit theorem is proved. The second one is when

{ϵ_{n}, n \in Z}

has general correlation structure: under mixing assumptions, we exhibit an estimator for the logarithm of the reproduction rate and we prove that it converges in quadratic mean with explicit speed. In addition, when the mixing coefficients decrease fast enough, we provide and prove a two terms expansion for the estimator. Numerical illustrations are provided.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.

期刊最新文献

Editorial Board Estimation of subcritical Galton Watson processes with correlated immigration Existence and uniqueness of SPDEs driven by nonlinear multiplicative mixed noise Editorial Board Conditional independence in stationary distributions of diffusions