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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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distribution of specific exponential functional of brownian motion

Does the following hold true $\forall T>0,a>0,c>0$ (in particular for c arbitrarily small): $P_0(\int_0^T e^{-aB_s}ds<{c})>0$? This is a minor result which will improve several steps in a couple …