$\ell^{\infty}$ Poisson invariance principles from two classical Poisson limit theorems and extension to non-stationary independent sequences

Aladji Babacar Niang; Gane Samb Lo; Chérif Mamadou Moctar Traoré; Amadou Ball

doi:10.16929/as/2022.3125.198

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arXiv · 2205.14541

$\ell^{\infty}$ Poisson invariance principles from two classical Poisson limit theorems and extension to non-stationary independent sequences

Aladji Babacar Niang·Gane Samb Lo·Chérif Mamadou Moctar Traoré·Amadou Ball

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Abstract

The simple Lévy Poisson process and scaled forms are explicitly constructed from partial sums of independent and identically distributed random variables and from sums of non-stationary independent random variables. For the latter, the weak limits are scaled Poisson processes. The method proposed here prepares generalizations to dependent data, to associated data in the first place.

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BibTeX RIS

Aladji Babacar Niang, Gane Samb Lo, Chérif Mamadou Moctar Traoré, Amadou Ball. 2022-05-28. $\ell^{\infty}$ Poisson invariance principles from two classical Poisson limit theorems and extension to non-stationary independent sequences. https://doi.org/10.16929/as%2F2022.3125.198

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