提出了截断Levy随机游动的连续马尔可夫模型。它概括了先前由Lubashevsky等人Phys.Rev.E79，011110（2009）; 80，031148（2009），Eur. J. B 78，207（2010），其允许在怀疑粒子运动中的非线性摩擦和取决于粒子速度的噪声强度的饱和。这两种效应都有自己的理由被认为是，并单独产生截断Levy随机游动的文件中所示。采用1.5阶强随机Runge-Kutta方法数值求解了控制颗粒运动的非线性Langevin方程，并利用所得数值数据计算了一定时间间隔内颗粒位移的几何平均值，构造了其分布函数。它表明，几何平均值的时间依赖性包括三个片段，随着时间尺度的增加，可以被归类为弹道制度，列维型制度（超弹道，准弹道，或superdiffusive一个），和布朗粒子的标准运动。对于中间Levy型部分，粒子位移的分布被发现是广义Cauchy形式的截止。此外，随机游动的性质主要取决于摩擦系数和噪声强度的某一比值，而不是它们各自的特性。
英文摘要：
A continuous Markovian model for truncated Levy random walks is proposed. It generalizes the approach developed previously by Lubashevsky et al. Phys. Rev. E 79, 011110 (2009); 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010) allowing for nonlinear friction in wondering particle motion and saturation of the noise intensity depending on the particle velocity. Both the effects have own reason to be considered and individually give rise to truncated Levy random walks as shown in the paper. The nonlinear Langevin equation governing the particle motion was solved numerically using an order 1.5 strong stochastic Runge-Kutta method and the obtained numerical data were employed to calculate the geometric mean of the particle displacement during a certain time interval and to construct its distribution function. It is demonstrated that the time dependence of the geometric mean comprises three fragments following one another as the time scale increases that can be categorized as the ballistic regime, the Levy type regime (superballistic, quasiballistic, or superdiffusive one), and the standard motion of Brownian particles. For the intermediate Levy type part the distribution of the particle displacement is found to be of the generalized Cauchy form with cutoff. Besides, the properties of the random walks at hand are shown to be determined mainly by a certain ratio of the friction coefficient and the noise intensity rather then their characteristics individually.
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School of Science and Engineering, Tokyo Denki University（东京电机大学理工学部）；The University of Tokyo（东京大学）；SoftBank Robotics Group Corp.（软银机器人集团公司）；Shinshu University（信州大学）；Waseda University（早稻田大学）
