Asymptotic results for a multivariate version of the alternative fractional Poisson process

作者：Beghin Luisa; Macci Claudio^*

来源：Statistics & Probability Letters, 2017, 129: 260-268.

DOI：10.1016/j.spl.2017.06.009

• Large deviations
• Moderate deviations
• Weighted Poisson distribution
• First kind error probability

A multivariate fractional Poisson process was recently defined in Beghin and Macci (2016) by considering a common independent random time change for a finite dimensional vector of independent (non-fractional) Poisson processes; moreover it was proved that, for each fixed t >= 0, it has a suitable multinomial conditional distribution of the components given their sum. In this paper we consider another multivariate process {(M) under bar (nu) (t) = (M-1(nu)(t), ... , M-m(nu)(t)) : t >= 0} with the same conditional distributions of the components given their sums, and different marginal distributions of the sums; more precisely we assume that the one-dimensional marginal distributions of the process {Sigma M-m(i=i)i(nu)(t): >= 0) coincide with the ones of the alternative fractional (univariate) Poisson process in Beghin and Macci (2013). We present large deviation results for {(M) under bar (nu) (t) = (M-1(nu)(t), ... , M-m(nu)(t)) : t >= 0}, and this generalizes the result in Beghin and Macci (2013) concerning the univariate case. We also study moderate deviations and we present some statistical applications concerning the estimation of the fractional parameter nu.

• 出版日期2017-10