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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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Expectation of time integral of Wiener process
I am trying to calculate $E(\int_0^T {W_s ds})$, where $W_s$ is a standard Brownian motion.
Now two approaches I can think of:
1) Take a partition of $[0,T]$. Calculate $E(\sum {W_{t_i}(t_{i+1} - t_ …