I'm in trouble with the following integral equation:
$$\phi(t)=\rho\int_0^1 t^2 s \phi(s)^2 ds+\nu(t)$$
where $\nu(t)$ is a white gaussian noise with variance $\sigma$ and mean value $\mu$. Is it possible to solve this equation in a closed form? Alternatively, can you obtain some property of the spectrum of $\phi(t)$ without solve it?
Thanks for any suggestion