Fast-slow dynamical systems are useful tools to describe various real life scenarios. The presence of slow variables that can have strong influence on fast ones makes the study of early warning signs an important field. This talk on my master's thesis seeks to deepen the study of early warning signs of stochastic partial differential equations (SPDEs), focusing on multiplication operators defined by analytic functions $f$. The studied early warning sign takes the form of changes in the variance as the bifurcation point is approached, especially divergence and its rate. The focus is on the study of analytic functions with domains in different dimensions. For a one-dimensional domain we obtain precise rates of divergence. In the case of the two- and three-dimensional domain an upper bound is obtained. These results are cross-validated by numerical simulations. Such theory can be very useful for several applications, such as epileptic seizures or voltage collapses in power systems