How does one describe a time-varying statistical spectrum: Transforming stochastic differential equations into phase-space

We address some fundamental issues regarding nonstationary stochastic processes. Among the questions we discuss are how one describes a nonstationary process and how one obtains a governing differential equation for it. We argue that a simplification occurs when one studies stochastic process in the time-frequency phase space. This leads to a number of interesting questions. How can one obtain the equations of motion for reduced quantities such as the mean and variance of a nonstationary stochastic process? How can one define local stationarity? How can nonstationary stochastic systems be modeled from experimental data? Among other questions.