We show that the Bernoulli part extraction method can be used to obtain approximate forms of the local limit theorem for sums of independent lattice valued random variables, with effective error term. That is with explicit parameters and universal constants. We also show that our estimates allow us to recover Gnedenko and provide a version with effective bounds of Gamkrelidze’s local limit theorem. We further establish by this method a local limit theorem with effective remainder for random walks in random scenery.

Approximate local limit theorems with effective rate and application to random walks in random scenery

Rita Giuliano
Primo
2017-01-01

Abstract

We show that the Bernoulli part extraction method can be used to obtain approximate forms of the local limit theorem for sums of independent lattice valued random variables, with effective error term. That is with explicit parameters and universal constants. We also show that our estimates allow us to recover Gnedenko and provide a version with effective bounds of Gamkrelidze’s local limit theorem. We further establish by this method a local limit theorem with effective remainder for random walks in random scenery.
2017
Giuliano, Rita
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/892959
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact