Frontiers of Mathematics in China >
Uniform Cramér moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment
Received date: 11 Feb 2020
Accepted date: 10 Oct 2020
Published date: 15 Oct 2020
Copyright
Let be a supercritical branching process in an independent and identically distributed random environment. We prove Cramér moderate deviations and Berry-Esseen bounds for log() uniformly in ,which extend the corresponding results by I. Grama, Q. Liu, and M. Miqueu [Stochastic Process. Appl., 2017, 127: 1255–1281] established for . The extension is interesting in theory, and is motivated by applications. A new method is developed for the proofs; some conditions of Grama et al. are relaxed in our present setting. An example of application is given in constructing confidence intervals to estimate the criticality parameter in terms of log() and n.
Xiequan FAN , Haijuan HU , Quansheng LIU . Uniform Cramér moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment[J]. Frontiers of Mathematics in China, 2020 , 15(5) : 891 -914 . DOI: 10.1007/s11464-020-0868-3
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