एप्लाइड और कम्प्यूटेशनल गणित जर्नल

Segmenting Fractional Lévy Stable Motion

Abstract

Duan Wang*

Fractional Lévy Stable Motion (FLSM) is an extension of the Lévy Stable Motion (LSM) that incorporates the concept of fractional dynamics, offering a rich framework for modeling various complex phenomena in fields such as finance, physics, and signal processing. Unlike Brownian motion, which is characterized by Gaussian increments, Lévy Stable Motion allows for heavy-tailed distributions, making it a more versatile tool for capturing real-world anomalies and extreme events. Fractional Lévy Stable Motion further extends this by introducing memory and long-range dependence, described by the Hurst parameter.