I came across this sub-question as a part of a bigger question, the question itself seems very simple but I'm having hard time figuring out a solution. Just to give a little background, this comes in a problem set in a master degree level stochastic process course.
I was asked to calculate $$ \lim\limits_{t \to \infty}E[1/P_t] $$ Where $$ dP_t={1 \over P_t}dt+dW_t $$ and $W_t$ is a standard Brownian motion and $P_0>0$
The answer is apparently 0, although I'm not quite sure how to prove this result.
Many thanks.