Work

The Lamperti transformation for self-similar processes : Dedicated to the memory of Stamatis Cambanis)

Year: 1997

Type: article

Abstract: In this paper we establish the uniqueness of the Lamperti transformation leading from self-similar to stationary processes, and conversely. We discuss ＄￥alpha＄-stable processes, which allow to understand better the difference between the Gaussian and non-Gaussian cases. As a by-product we get a natural construction of two distinct ＄￥alpha-＄ stable Ornstein-Uhlenbeck processes via the Lamperti transformation for ＄0<￥alpha<2＄ . Also a new class of mixed linear fractional ＄￥alpha＄-stable motions is introduced.

Source: Yokohama National University Repository (Yokohama National University)

Authors: Krzysztof Burnecki, Makoto Maejima, Aleksander Weron

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W413333980

FWCI: 0.53

Cites:

Cited by: 10

Related to: 10