Given $dG_{t}=\alpha S_{t}dt+\upsilon S_{t}dW_{t}$ and $dS(t)={dG_{t}}-\epsilon_{t}dt$. How can I have $S_{t}=\mathbb{E}^{\mathbb{Q}}\left[\int_{t}^{+\infty}e^{-r(s-t)}\epsilon_{t}ds|\mathcal{F}_{t}\right]$ where $W_{t}^{\mathbb{Q}}=W_{t}+\int_{0}^{t}\frac{\alpha-r}{\upsilon}ds$
Itô's lemma to solve the SDE
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stochastic-processes
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1Please, specify what is Q. – 2012-12-30
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0Tarasenya, $\mathbb Q$ is completely determined by the definition of the brownien motion under $\mathbb Q$,it's a consequense of Girsanov theorem as you can see in my answer. – 2012-12-31
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0What is still mysterious is $r$. – 2012-12-31