Non-central moderate deviations for compound fractional Poisson processes

Statistics and Probability Letters - Tập 185 - Trang 109424 - 2022
Luisa Beghin1, Claudio Macci2
1Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
2Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Rome, Italy

Tài liệu tham khảo

Beghin, 2013, Large deviations for fractional Poisson processes, Statist. Probab. Lett., 83, 1193, 10.1016/j.spl.2013.01.017 Beghin, 2009, Fractional Poisson processes and related planar random motions, Electron. J. Probab., 14, 1790, 10.1214/EJP.v14-675 Beghin, 2010, Poisson-type processes governed by fractional and higher-order recursive differential equations, Electron. J. Probab., 15, 684, 10.1214/EJP.v15-762 Dembo, 1998 Duffy, 2011, Sample path large deviations of Poisson shot noise with heavy-tailed semiexponential distributions, J. Appl. Probab., 48, 688, 10.1017/S002190020000824X Gantert, 1998, Functional erdös-renyi laws for semiexponential random variables, Ann. Probab., 26, 1356, 10.1214/aop/1022855755 Giuliano, 2021 Glynn, 1994, Large deviations behavior of counting processes and their inverses, Queueing Syst. Theory Appl., 17, 107, 10.1007/BF01158691 Gorenflo, 2014, Mittag-Leffler functions Leonenko, 2021, Large deviations for a class of tempered subordinators and their inverse processes, Proc. Roy. Soc. Edinburgh Sect. A, 151, 2030, 10.1017/prm.2020.95 Leonenko, 2014, Correlation structure of time-changed Lévy processes, Commun. Appl. Ind. Math., 6 Meerschaert, 2002, Stochastic solution of space–time fractional diffusion equations, Phys. Rev. E, (3) 65, 10.1103/PhysRevE.65.041103 Meerschaert, 2011, The fractional Poisson process and the inverse stable subordinator, Electron. J. Probab., 16, 1600, 10.1214/EJP.v16-920 Meerschaert, 2004, Limit theorems for continuous-time random walks with infinite mean waiting times, J. Appl. Probab., 41, 623, 10.1239/jap/1091543414 Oliveira, 2021, Fractional Poisson random sum and its associated normal variance mixture Orsingher, 2012, The space-fractional Poisson process, Statist. Probab. Lett., 82, 852, 10.1016/j.spl.2011.12.018 Stabile, 2010, Large deviations of Poisson shot noise processes under heavy tail semi-exponential conditions, Statist. Probab. Lett., 80, 1200, 10.1016/j.spl.2010.03.017 Vellaisamy, 2018, Fractional negative binomial and Pólya processes, Probab. Math. Statist., 38, 77, 10.19195/0208-4147.38.1.5