Within the numerical simulation method applied to the Langevin equation, the escape problem of particle moving in the truncated quartic potential driven by two types of correlated Lévy noise, i.e., Ornstein–Uhlenbeck Lévy noise and harmonic velocity Lévy noise, is studied. The dependence of the escape rate on the noise intensity parameter, the Lévy index, the noise correlation, and the particle mass is discussed. Results reveal that the correlation, especially the strong correlation, makes the power-law exponent \(\alpha (\mu )\) and the inverse coefficient \(\text {lnc}(\mu )\) present significantly different dependences on the Lévy index \(\mu \). Especially, because of the distinctly opposite correlation properties of these two noises, the escape rate shows entirely opposite phenomena, i.e., the escape rate of the particles driven by the Ornstein–Uhlenbeck Lévy noise decreases with correlation increasing, whereas the escape rate of the particles driven by the harmonic velocity Lévy noise increases instead. Since the particle becomes heavy with m increasing, for the two types of correlated Lévy flight, the escape rates both decrease monotonically with particle mass increasing.

在应用于朗之万方程的数值模拟方法中，研究了由两种相关的 Lévy 噪声，即 Ornstein-Uhlenbeck Lévy 噪声和谐波速度 Lévy 噪声驱动的粒子在截断四次势中运动的逃逸问题。讨论了逃逸率对噪声强度参数、Lévy 指数、噪声相关性和粒子质量的依赖性。结果表明，相关性，尤其是强相关性，使得幂律指数\(\alpha (\mu )\)和逆系数\(\text {lnc}(\mu )\)对列维指数\(\mu \). 特别是，由于这两种噪声明显相反的相关性，逃逸率表现出完全相反的现象，即 Ornstein-Uhlenbeck Lévy 噪声驱动的粒子逃逸率随着相关性的增加而降低，而粒子逃逸率由谐波速度驱动的 Lévy 噪声反而增加。由于粒子随着m 的增加而变重，对于两种相关的 Lévy 飞行，逃逸率都随着粒子质量的增加而单调下降。