11 citations · 20 across the 6 of their papers we have counts for
6 papers
Classical and Almost Sure Local Limit Theorems
Zbigniew Szewczak, Michel Weber
We present and discuss the many results obtained concerning a famous limit theorem, the local limit theorem, which has many interfaces, with Number Theory notably, and for which, i…
Truncated moments of perpetuities and a new central limit theorem for GARCH processes without Kesten's regularity
Adam Jakubowski, Zbigniew S. Szewczak
We consider a class of perpetuities which admit direct characterization of asymptotics of the key truncated moment. The class contains perpetuities without polynomial decay of tail…
A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law
Rita Giuliano, Zbigniew S. Szewczak
In the present paper we obtain a new correlation inequality and use it for the purpose of extending the theory of the Almost Sure Local Limit Theorem to the case of lattice random…
Almost Sure Local Limit Theorem for the Dickman distribution
Rita Giuliano, Zbigniew Szewczak, Michel Weber
In this paper we present a new correlation inequality and use it for proving an Almost Sure Local Limit Theorem for the so-called Dickman distribution. Several related results are…
Edgeworth expansions in operator form
Zbigniew S. Szewczak
An operator form of asymptotic expansions for Markov chains is established. Coefficients are given explicitly. Such expansions require a certain modification of the classical spect…
On limit theorems for continued fractions
Zbigniew S. Szewczak
It is shown that for sums of functionals of digits in continued fraction expansion the Kolmogorov-Feller weak laws of large numbers and the Khinchine-Lévy-Feller-Raikov characteriz…