How to compute $E[1/x]$, where the process is described by $dx = ax\,dt + b\,dw$?

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I am quite new to stochastict calculus and probability and therefore my question may be naive.

I have a process described by $dx= ax\,dt + b\,dw$ and I would like to compute $\operatorname E\left[\dfrac{1}{x_t}\right]$.

Can anyone give me some hints on how proceed (even numerically)?