Multidimensional Probability Density of a Signal Which is Phase (Frequency) Modulated by a Random Process

The $n$-dimensional probability density of a signal phase (frequency) modulated by a random process is determined. As an example an expression is given for the two-dimensional probability density of a signal phase modulated by a stationary normal random process or by a harmonic oscillation with random initial phase in the interval $(0,2\pi)$