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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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convergence in distribution of stochastic gradient descent.

I think you're talking about the SPGD algorithm as mentioned in Vorontsov's papers. As far as I now there is no real mathematical background theory directly for this, but there exist theory about SPSA …
Johannes L's user avatar