Statistics of a filtered telegraph signal

Equations are derived which describe the time evolution of the probability density and corresponding characteristic function of a telegraph signal whi ch has passed through a detuned Lorentzian filter. A closed form expression for the characteristic function is obtained for the tuned case and the pre dicted joint statistics and correlation properties are reviewed in the cont ext of earlier results. Low-order correlation properties for the more gener al detuned case are calculated. It is shown that the stationary single inte rval statistics can be generated by a random phasor moving in a space of fr actional dimensions and that a simple transform of variable leads to distri butions which are stable in this space.