Brownian Motion, Martingales, and Stochastic Calculus

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Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions (2022, methodology): “We also use the following notion from stochastic calculus [Le 16, Deﬁnition 4.6]: • A local martingale ( L t ) t ∈ [0 ,T ] is a stochastic process s.t. there exists a sequence of nondecreasing stopping times T n → T s.t.”