Heteroskedastic Levy Flights

TL;DR

This paper investigates truncated Levy flights with heteroskedastic variance fluctuations, highlighting their slow transition to Gaussian behavior and potential applications in economic time series modeling.

Contribution

It introduces a model of heteroskedastic truncated Levy flights, analyzing how correlated variance fluctuations affect the crossover to Gaussian distributions.

Findings

Crossover to Gaussian regime occurs at larger times with heteroskedasticity.

Correlated variance fluctuations slow down the convergence to Gaussian behavior.

Potential applications in modeling economic time series with heavy tails.

Abstract

Truncated L\'{e}vy flights are random walks in which the arbitrarily large steps of a L\'{e}vy flight are eliminated. Since this makes the variance finite, the central limit theorem applies, and as time increases the probability distribution of the increments becomes Gaussian. Here, truncated L\'{e}vy flights with correlated fluctuations of the variance (heteroskedasticity) are considered. What makes these processes interesting is the fact that the crossover to the Gaussian regime may occur for times considerably larger than for uncorrelated (or no) variance fluctuations. These processes may find direct application in the modeling of some economic time series.