  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.

Statistical Mechanics;General Finance