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

An analytic expression for characteristic function defining a truncated 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)]. With the analytic expression for the characteristic function, the convergence of the Levy process towards the Gaussian is demonstrated without simulations. In the calculation of first return probability the simulations are replaced by numerical integration using simple quadratures.