An Introduction to Stochastic Dynamics

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Two-time-scales hyperbolic–parabolic equations driven by Poisson random measures: Existence, uniqueness and averaging principles (2017, background): “It is well known nowadays that much evidence has been gathered that Poisson jumps are ubiquitous in modelling uncertainty in many diverse fields of science [1, 25, 13].”
A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networks (2019, background): “, 2012), audio signals (Liutkus & Badeau, 2015), the assumption might fail to hold (see (Duan, 2015) for more examples).”
Asynchronous Stochastic Quasi-Newton MCMC for Non-Convex Optimization (2018, background): “The assumptions H1 and H2 are standard conditions in analysis of SDEs (Duan, 2015) and similar assumptions have also been considered in stochastic gradient (Moulines & Bach, 2011) and stochastic L-BFGS algorithms (Zhou et al.”