We investigate the first-passage dynamics of symmetric and asymmetric Lévy flights in semi-infinite and bounded intervals. By solving the space-fractional diffusion equation, we analyse the fractional-order moments of the first-passage time probability density function for different values of the index of stability and the skewness parameter. A comparison with results using the Langevin approach to Lévy flights is presented. For the semi-infinite domain, in certain special cases analytic results are derived explicitly, and in bounded intervals a general analytical expression for the mean first-passage time of Lévy flights with arbitrary skewness is presented. These results are complemented with extensive numerical analyses.

中文翻译：

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不对称莱维航班的首次通过时刻

我们研究半无限和有界区间中对称和不对称Lévy飞行的初次通过动力学。通过求解空间分数阶扩散方程，我们针对稳定性指数和偏度参数的不同值，分析了首次通过时间概率密度函数的分数阶矩。提出了使用兰格文方法进行Lévy航班的结果的比较。对于半无限域，在某些特殊情况下，将明确得出分析结果，并在有界区间内，给出具有任意偏度的Lévy航班平均首次通过时间的一般解析表达式。这些结果得到了广泛的数值分析的补充。