Impact of non-symmetric α-stable Lévy processes on mean exit time in abrupt climate transitions

Abrupt climate change involves rapid transitions between alternative stable states in the Earth's climate system, posing significant risks to global stability. Recent concerns suggest that such transitions could be triggered by individual extreme events, yet the underlying mechanisms remain poorly understood. In this study, we investigate these mechanisms using a stochastic energy balance model that incorporates extreme weather events through a non-symmetric α-stable Lévy process. Our analysis highlights the critical role of the non-symmetric Lévy parameters in shaping system dynamics. Specifically, the stability parameter α governs the frequency and intensity of extreme events: smaller α values lead to larger but less frequent extreme events, significantly shortening the mean exit time (MET) of the system. Furthermore, the skewness parameter β determines the asymmetric distribution of extreme events, with its impact highly dependent on tail heaviness: environments dominated by heavy-tailed (α