@inbook{890e08764c4e41468ef8b8f89499ea2b,
title = "The brownian motion on aff(R) and quasi-local theorems",
abstract = "This paper is concerned with Random walk approximations of the Brownian motion on the Affine group Aff(R). We are in particular interested in the case where the innovations are discrete. In this framework, the return probabilities of the walk have fractional exponential decay in large time, as opposed to the polynomial one of the continuous object. We prove that integrating those return probabilities on a suitable neighborhood of the origin, the expected polynomial decay is restored. This is what we call a Quasi-local theorem.",
keywords = "Affine group, Heat-kernel bounds, Local and quasi local limit theorems, Random walks and Brownian motion",
author = "V. Konakov and S. Menozzi and S. Molchanov",
note = "Publisher Copyright: {\textcopyright}2019 American Mathematical Society.",
year = "2019",
month = jan,
day = "1",
doi = "10.1090/conm/739/14895",
language = "English",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "97--124",
booktitle = "Contemporary Mathematics",
}