What is the expected value of the following process: $$ e^{\int_0^t B_u\, du} $$
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2026-03-31 05:03:41.1774933421
Expected Value of the exponential of a stochastic integral
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See here for the fact that $\int_0^t B_u du$ follows the normal distribution with zero mean and variance $\dfrac{t^3}{3}$.
See here for moment generating function(MGF) of normal distribution