Gaussian $f$-regular processes and asymptotic behavior of likelihood function

Let $P_t^f$ – be a measure generated by a stationary Gaussian process with spectral density $f$ on time interval lenght $t$, and $L_t=\ln\frac{dP_t^f}{dP_t^{f_0}}$ be likelihood function. We investigate a correspondence between asymptotic behavior of function $L_t$ and some regularity condition of process $x$.