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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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Is there a probability theory developed in intuitionistic logic?
There is a probability theory developed in Łukasiewicz logic.
If you understand the french (and if you are still interested):
http://www.brunodefinetti.it/Opere/logiquedelaProbabilite.pdf