Non-central moderate deviations for compound fractional Poisson processes. (English) Zbl 1493.60052
Moderate deviations often mean a class of deviation principles that fills the gap between a convergence in probablity to zero governed by a large deviation principle and a weak convergence to a centered Gaussian distribution. When the centered Gaussian distribution is replaced by a non-Gaussian distribution, the authors call the corresponding deviation principle non-central moderate deviations. In this paper, the authors study non-central moderate deviations for compound fractional Poisson processes with light-tailed jumps.
Reviewer: Renming Song (Urbana)
MSC:
| 60F10 | Large deviations |
| 60F05 | Central limit and other weak theorems |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 33E12 | Mittag-Leffler functions and generalizations |
Keywords:
Mittag-Leffler function; inverse of a subordinator; weak convergence; non-central moderate deviationsReferences:
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