On the limit behaviour of the solution of a stochastic diffusion equation

The probability density of the limit distribution of the process $f(\xi(tT))/\sqrt T$ as $T\to\infty$ is found where
$$ f(x)=\int_0^x\exp\biggl\{-2\int_{-\infty}^y\biggl[\frac{a(u)}{\sigma^2(u)}-\frac12\frac{\sigma'(u)}{\sigma(u)}\biggr]\,du\biggr\}\frac{dy}{\sigma(y)}, $$
and $\xi(t)$ is the solution of stochastic diffusion equation (1).