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The Lamperti transformation for self-similar processes

By Krzysztof Burnecki, Makoto Maejima and Aleksander Weron

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 0Lamperti transformation; Self-similar process; Stationary process; Stable distribution;

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