A central limit theorem for martingales and an application to branching processes

DOI10.1016/0304-4149(78)90021-2zbMath0373.60023OpenAlexW1994264400MaRDI QIDQ1244739

David John Scott

Publication date: 1978

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(78)90021-2

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Markov processes: estimation; hidden Markov models (62M05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (14)

Branching processes. I ⋮ Joint estimation of the offspring mean and offspring variance of a second order branching process ⋮ Asymptotic inference for non-supercritical partially observed branching processes ⋮ A test for randomness of the environments in a branching process ⋮ Estimation of growth rate in second order branching process ⋮ Unnamed Item ⋮ Joint estimation of offspring mean and offspring variance of controlled branching process ⋮ Estimation in continuous state-space branching processes ⋮ Weak convergence results for multiple generations of a branching process ⋮ Functional limit theorems for marked Hawkes point measures ⋮ Statistical inference for partially observed branching processes with immigration ⋮ On an optimal asymptotic property of the maximum likelihood estimator of a parameter from a stochastic process ⋮ Estimation in second order branching processes with application to swine flu data ⋮ Asymptotic inference for partially observed branching processes

Cites Work

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• On mixing sequences of sets
• Estimation of the mean and the initial probabilities of a branching process
• Maximum likelihood estimation for stochastic processes - a martingale approach
• Zu einigen Konvergenzeigenschaften von Folgen zufälliger Elemente
• Übertragung von Grenzaussagen für Folgen zufälliger Elemente auf Folgen mit zufälligen Indizes
• An invariance principle and some convergence rate results for branching processes

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