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math.PR2022
Lower bounds for variances of Poisson functionals
Matthias Schulte, Vanessa Trapp
Lower bounds for variances are often needed to derive central limit theorems. In this paper, we establish a lower bound for the variance of Poisson functionals that uses the differ…
math.PR2022
Dickman Approximation of weighted random sums in the Kolmogorov distance
Chinmoy Bhattacharjee, Matthias Schulte
We consider distributional approximation by generalized Dickman distributions, which appear in number theory, perpetuities, logarithmic combinatorial structures and many other area…
math.PR2022★ 3 cited
Normal approximation of Kabanov-Skorohod integrals on Poisson spaces
Günter Last, Ilya Molchanov, Matthias Schulte
We consider the normal approximation of Kabanov-Skorohod integrals on a general Poisson space. Our bounds are for the Wasserstein and the Kolmogorov distance and involve only diffe…