We present an analytically tractable scheme to solve the mean transition path shape and mean transition path time of one-dimensional stochastic systems driven by Poisson white noise. We obtain the Fokker-Planck operator satisfied by the mean transition path shape. Based on the non-Gaussian property of Poisson white noise, a perturbation technique is introduced to solve the associated Fokker-Planck equation. Moreover, the mean transition path time is derived from the mean transition path shape. We illustrate our approximative theoretical approach with the three paradigmatic potential functions: linear, harmonic ramp, and inverted parabolic potential. Finally, the Forward Fluxing Sampling scheme is applied to numerically verify our approximate theoretical results. We quantify how the Poisson white noise parameters and the potential function affect the symmetry of the mean transition path shape and the mean transition path time.

我们提出了一种解析可解决的方案，以解决由泊松白噪声驱动的一维随机系统的平均过渡路径形状和平均过渡路径时间。我们获得平均过渡路径形状满足的Fokker-Planck算子。基于泊松白噪声的非高斯性质，引入了一种摄动技术来求解相关的福克-普朗克方程。此外，平均过渡路径时间是从平均过渡路径形状导出的。我们用三个范式势函数来说明我们的近似理论方法：线性，谐波斜坡和反抛物线势。最后，采用正向流星采样方案对我们的近似理论结果进行数值验证。