Let $B\left(s\right)$ be a brownian motion and $\sigma\left(s\right)$ be the nondeterministic function. The following equation then holds $ \mathbb{E}\left(\exp\left(i\int_{0}^{t}\sigma\left(s\right)\, e^{-a\left(t-s\right)}dB\left(s\right)\right)\right)=\mathbb{E}\left(\exp\left(-\frac{1}{2}\int_{0}^{t}\sigma^{2}\left(s\right)\, e^{-2a\left(t-s\right)}ds\right)\right) $
How can i prove this equality? i'm quite stuck here.
Thanks