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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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Does there exist an almost surely differentiable martingale?
Others have answered that there does not exist an a.s. differentiable martingale process that's not constant. One related fact (not asked for but interesting) is that an a.s. differentiable Markov pro …