I was told recently that we can't (or shouldn't) take the reciprocal of a stochastic parameter with white noise. Specifically, if we have a stochastic parameter $\lambda_t$ $$ \lambda_t = \lambda_0 + \delta W_t $$ where $\lambda_0 \ne 0$ is fixed and $\delta W_t$ is white noise (Wiener increment) with $|\delta W_t| \ll |\lambda_0$|, then we shouldn't ever write $1/\lambda_t$.
Why is this the case? What 'breaks' when we try to take the inverse of white noise? A related question is whether $1/\delta W_t$ is a meaningful quantity at all or simply undefined.