I. Koponen, ANALYTIC APPROACH TO THE PROBLEM OF CONVERGENCE OF TRUNCATED LEVY FLIGHTS TOWARDS THE GAUSSIAN STOCHASTIC-PROCESS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(1), 1995, pp. 1197-1199
An analytic expression for characteristic function defining a truncate
d Levy flight is derived. It is shown that the characteristic function
yields results in agreement with recent simulations of truncated Levy
flights by Mantegna and Stanley [Phys. Rev. Lett. 73, 2946 (1994)]. W
ith the analytic expression for the characteristic function, the conve
rgence of the Levy process towards the Gaussian is demonstrated withou
t simulations. In the calculation of first return probability the simu
lations are replaced by numerical integration using simple quadratures
.