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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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Exit probability on a finite interval

I have a question about the estimate of the exit probability on a finite interval. Given a $q$ function bounded and continuous, given the following SDE \begin{cases} dX_s=(\beta-q(s))X_sds+\frac{1}{2 …