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Markov分支过程的调和矩
Harmonic Moments for the Supercritical Markov Branching Processes

DOI: 10.12677/PM.2022.121016, PP. 117-124

Keywords: Markov分支过程，上临界，调和矩，大偏差
Markov Branching Process, Supercritical, Harmonic Moment, Large Deviation

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Abstract:

假设{Z(t);t≥0}是上临界的Markov分支过程，本文主要研究了该过程调和矩的收敛速率，研究发现，该收敛速度存在相变，并且该相变取决于mr+b1 > 0，mr+b1=0或mr+b1 < 0；作为应用，本文还进一步讨论了Z(t+s)/Z(t)的大偏差速率。
Suppose that {Z(t);t≥0} be a supercritical Markov branching process. The paper mainly studies the convergence rate of the harmonic moment of the process. We find that there is a phase transition for convergence rates, which depends on mr+b1 > 0, =0 or < 0. As an application, the large deviation rate Z(t+s)/Z(t) is discussed in this paper.

References

[1]  Heyde, C.C. and Brown, B.M. (1971) An Invariance Principle and Some Convergence Rate Results for Branching Processes. Probablility Theory and Related Fields, 20, 271-278.
https://doi.org/10.1007/BF00538373
[2]  Nagaev, A.V. (1967) On Estimating the Expected Number of Direct Descendants of a Particle in a Branching Process. Theory of Probability and Its Applications, 12, 314-320.
https://doi.org/10.1137/1112037
[3]  Pakes, A.G. (1975) Non-Parametric Estimation in the Galton-Watson Process. Mathematical Biosciences, 26, 1-18.
https://doi.org/10.1016/0025-5564(75)90091-7
[4]  Ney, P.E. and Vidyashankar, A.N. (2003) Harmonic Moments and Large Deviation Rates for Supercritical Branching Processes. The Annals of Applied Probability, 13, 475-489.
https://doi.org/10.1214/aoap/1050689589
[5]  Sun, Q. and Zhang, M. (2017) Harmonic Moments and Large Deviations for Supercritical Branching Processes with Immigration. Frontiers of Mathematics in China, 12, 1201-1220.
https://doi.org/10.1007/s11464-017-0642-3
[6]  Ney, P.E. and Vidyashankar, A.N. (2004) Local Limit Theory and Large Deviations for Supercritical Branching Processes. The Annals of Applied Probability, 14, 1135-1166.
https://doi.org/10.1214/105051604000000242
[7]  Athreya, K.B. (1994) Large Deviation Rates for Branching Processes: I. Single Type Case. The Annals of Applied Probability, 4, 779-790.
https://doi.org/10.1214/aoap/1177004971
[8]  Ling, J.N. and Zhang, M. (2016) Large Deviation for Supercritical Branching Processes with Immigration. Acta Mathematica Sinica English, 32, 893-900.
https://doi.org/10.1007/s10114-016-5437-z
[9]  Athreya, K.B. and Ney. P.E. (1972) Branching Processes.
https://doi.org/10.1007/978-3-642-65371-1
[10]  Asmussen, S. and Hering, H. (1983) Branching Processes.
https://doi.org/10.1007/978-1-4615-8155-0

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