Autocorrelation function of phase modulated wiener process

Question

How to find the autocorrelation function $R_x(\tau)=E[X(t_1)X^*(t_2)]$ of phase modulated Winner random process oscillation $X\left( t \right)=\exp \left\{ j\varphi \left( t \right) \right\}$, where $\varphi \left( t \right)=2\pi \int\limits_{0}^{t}{\dot{n}\left( u \right)du}$?
And how to find ACF ${{R}_{y}}\left( {{\tau }_{1}} \right)$ of process $Y\left( t,{{\tau }_{1}} \right)=X\left( t \right){{X}^{*}}\left( t+{{\tau }_{1}} \right)$, which is a signal at the output of the RF downconverted mixer to the first input of which the signal $X(t)$ is being sent, and to the second one its delayed copy for a while $\tau_1$ ?