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I am trying to calculate a stochastic integral $\mathbb{E}[\int_0^t e^{as} dW_s]$. I tried breaking it up into a Riemann sum $\mathbb{E}[\sum e^{as_{t_i}}(W_{t_i}-W_{t_{i-1}})]$, but I get expected value of $0$, since $\mathbb{E}(W_{t_i}-W_{t_{i-1}}) =0$. But I think it's wrong. Thanks!

And I want to calculate $\mathbb{E}[W_t \int_0^t e^{as} dW_s]$ as well, I write $W_t=\int_0^t dW_s$ and get $\mathbb{E}[W_t \int_0^t e^{as} dW_s]=\mathbb{E}[\int_0^t e^{as} dW_s]$.

Is that ok?

($W_t$ is brownian motion.)

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    @Srivatsan: $W_s$ is very common notation for standard Brownian motion or *Wiener process* (http://en.wikipedia.org/wiki/Wiener_process)2011-10-26
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    And the expected value is zero, for the reason mentioned in the question (although to be rigorous you should be careful taking the limit).2011-10-26
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    I think our [stochastic integral] tread is quite poor, so maybe we can re-tag appropriate question with this tag.2011-10-26

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