Transition path properties for one-dimensional systems driven by Poisson white noise. (December 2020) - Li, Hua; Xu, Yong; Metzler, Ralf; Kurths, Jürgen
Highlights: We present an analytic scheme of mean TPS, TPT under Poisson white noise. The proposed scheme strongly extends the methods to solve the mean TPT and TPS. Three paradigmatic potential functions are illustrated. The corresponding theoretical results are verified by the Forward Flux Sampling. We quantify the effects of Poisson white noise parameters and potential function. Abstract: 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.