Cumulant Approach of Arbitrary Truncated Levy Flight

TL;DR

This paper develops a cumulant-based method to describe arbitrary truncated Levy flights, analyzing how different truncation shapes affect their properties in Gaussian and Levy regimes.

Contribution

It introduces a cumulant approach for arbitrary truncation in Levy flights and investigates the impact of truncation shape on their statistical properties.

Findings

Cumulants for truncated Levy distributions are explicitly derived.

Truncation shape significantly influences Levy flight behavior.

The method applies to both Gaussian and Levy regimes.

Abstract

The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gaussian and the Levy regimes has been investigated.