ANALYTIC APPROACH TO THE PROBLEM OF CONVERGENCE OF TRUNCATED LEVY FLIGHTS TOWARDS THE GAUSSIAN STOCHASTIC-PROCESS

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 .