${\ell }^{\infty }$ 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 +1

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-stati…