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The dynamics of the Earth's magnetosphere exhibits strongly fluctuating patterns as well as non-stationary and non-linear interactions, more pronounced during magnetospheric substorms and magnetic storms. This complex dynamics comprises both stochastic and deterministic features occurring at different time scales. Here we investigate the stochastic nature of the magnetospheric substorm dynamics by analysing the Markovian character of SuperMAG SME and SML geomagnetic indices. By performing the Chapman-Kolmogorov test, the SME/SML dynamics appears to satisfy the Markov condition at scales below 60 minutes. The Kramers-Moyal analysis instead highlights that a purely diffusive process is not representative of the magnetospheric dynamics, thus a model that includes both diffusion and Poisson-jump processes is used to reproduce the SME dynamical features at small scales. A discussion of the similarities and differences between this model and the SME properties is provided with a special emphasis on the metastability of the Earth's magnetospheric dynamics. Finally, the relevance of our results in the framework of Space Weather is also addressed.