First exit times of SDEs driven by stable Lévy processes

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Lévy flights, non-local search and simulated annealing (2007, background): “... in our papers [Pav06b, Pav06a] we considered a continuous-time counterpart of the process ˆ Z driven by L´evy flights of stability index � ∈ (0,2), and temperature �(t) ∼ t −� , � > 0. We discovered that such a jump process never settles in the neighbourhood of a global minimum, but can be used ”
A Diffusion Theory for Deep Learning Dynamics: Stochastic Gradient Descent Escapes From Sharp Minima Exponentially Fast (2020, background): “The polynomial relation is a well studied conclusion in stochastic process (Imkeller and Pavlyukevich, 2006).”
A Diffusion Theory For Minima Selection: Stochastic Gradient Descent Escapes Sharp Minima Exponentially Fast (2020, background): “introduces the polynomial relation of the mean escape time and loss valleys’ width in the case of the isotropic Lévy noise. The polynomial relation is a well studied conclusion in stochastic process (Imkeller and Pavlyukevich, 2006). 3 Simsekli et al. (2019) ﬁrst argues that stochastic gradient nois”
First exit times for Lévy-driven diffusions with exponentially light jumps. (2007, background): “The concept of ε-dependent separation of small and large jump parts which already proved to be successful in [17] takes a central role, and is basic for the proof that, apart from a Gaussian part, small jumps do not alter the behavior of solution curves of the unperturbed dynamical system by much.”