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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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Branching Brownian Motion and the KPP equation
The answer given by Martin Hairer is perfect. But if you are not familiar with the not familiar with pdes, just differentiate the right hand side wrt to t. Note that when you differentiate the integra …