# solution to stochastic integral

Can I know how to compute the analytical solution (if exist) to the following integral? $$\int_0^t \exp(\alpha s - \sigma W_s) \; ds$$ and $$\int_0^t \exp(\alpha s - \sigma W_s) \; dW_s$$ I see these when trying to solve the following SDE $$dX_t = \theta(\mu - X_t) \; dt + (\epsilon + \sigma X_t) \; dW_t$$

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Hi Jason, Please read over the answer to meta.mathoverflow.net/questions/70/how-to-ask-page, and revise this question. Certainly questions on MO should address experts in the field, but they should also try to be self-contained. For example, what types of things are $\alpha, \sigma, \mu, \dots$? –  Theo Johnson-Freyd Jul 15 at 2:57