How Does One Describe A Time-Varying Statistical Spectrum: Transforming Stochastic Differential Equations Into Phase-Space
Lorenzo Galleani · AIP conference proceedings · 2005
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.