arXiv subjects

Zbigniew S. Szewczak

Publications and source records attributed to Zbigniew S. Szewczak.

4 recordsLinked to original sources

arXiv2020

Truncated moments of perpetuities and a new central limit theorem for GARCH processes without Kesten's regularity

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 probabilities and thus not satisfying Kesten's theorem. We show how to apply this result in deriving a new weak law of large numbers for solutions to stochastic recurrence equations and a new central limit theorem for GARCH(1,1) processes in the critical case.

math.PR↗

arXiv2013

A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law

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 sequences in the domain of attraction of a stable law. In particular, we prove ASLLT in the case of the normal domain of attraction of $α$--stable law, $α\in(1,2)$.

math.PR↗

arXiv2007

Edgeworth expansions in operator form

An operator form of asymptotic expansions for Markov chains is established. Coefficients are given explicitly. Such expansions require a certain modification of the classical spectral method. They prove to be extremely useful within the context of large deviations.

math.PR↗

arXiv2007

On limit theorems for continued fractions

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 characterization of the domain of attraction of the normal law hold.

math.PR↗