Analytic approach to the problem of convergence of truncated Levy flights towards the Gaussian stochastic process

Ismo Koponen

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Analytic approach to the problem of convergence of truncated Levy flights towards the Gaussian stochastic process

机译：截断征费飞行向高斯随机过程收敛的解析方法

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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.

机译：推导了特征函数的解析表达式，该函数定义了截短的征费飞行。结果表明，特征函数产生的结果与Mantegna和Stanley [Phys。牧师73，2946（1994）]。通过特征函数的解析表达式，无需模拟即可证明Levy过程向高斯收敛。在计算首次返回概率时，使用简单的正交函数将数值积分替换为模拟。

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《Physical review, E. Statistical physics, plasmas, fluids, and related interdisciplinary topics》 |1995年第1期|共3页
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Ismo Koponen;
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1. Analytic approach to the problem of convergence of truncated Levy flights towards the Gaussian stochastic process [J] . Ismo Koponen Physical review, E. Statistical physics, plasmas, fluids, and related interdisciplinary topics . 1995,第1期

机译：截断征费飞行向高斯随机过程收敛的解析方法
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3. Cumulant approach of arbitrary truncated Levy flight [J] . Vinogradov D.V. Physica, A. Statistical mechanics and its applications . 2010,第24期

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8. I,II Convergence and Rate of Convergence Theorems for Constrained and Unconstrained Stochastic Approximation,via Weak Convergence Methods. III Numerical Studies for Constrained Stochastic Approximation Problems, [R] . kushner,harold j. lakshmivarahan, s. 1977

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Analytic approach to the problem of convergence of truncated Levy flights towards the Gaussian stochastic process

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