Let $W$ be a standard Brownian motion. Why is $\xi = \frac{1}{W}$ not a valid Ito integrand?
Here is what seems to be an indirect argument. Suppose it is. Then $$ dW = W \xi dW. $$ So that $$ W_t = e^{\int_0^t \xi' dW_s - \frac12 \int_0^t |\xi'|^2 ds} > 0, \;\; $$ which is impossible. Is there a more direct argument using properties of Brownian paths?
The reciprocal normal distribution has no finite moments but why is localization not possible?