Deviations for Martingale Convergence of a Branching Process with Random Index

Deviations for Martingale Convergence of a Branching Process with Random Index

The purpose of this paper is to obtain large deviations, moderate deviations and normal deviations for the convergence of martingale generated by a supercritical Galton–Watson process with a Poisson process as its time index. Harmonic moments and Shröder index play an important role in the proofs....

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Veröffentlicht in:Bulletin of the Malaysian Mathematical Sciences Society 2020-09, Vol.43 (5), p.3499-3512
Hauptverfasser: Gao, Zhenlong, Wang, Min, Zhang, Huili
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Branching (mathematics)
Convergence
Martingales
Mathematics
Mathematics and Statistics
Stochastic processes
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Beschreibung
Zusammenfassung:The purpose of this paper is to obtain large deviations, moderate deviations and normal deviations for the convergence of martingale generated by a supercritical Galton–Watson process with a Poisson process as its time index. Harmonic moments and Shröder index play an important role in the proofs.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-019-00882-x