Heteroskedastic Levy Flights

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.