Time-frequency characterization of stochastic differential equations

Abstract

Time-frequency analysis provides an effective description of the nonstationary random processes arising from random phenomena. These phenomena have typically a time-varying spectral content, which can be represented by using time-frequency distributions. The stochastic differential equation that models the nonstationary random process can be transformed in the time-frequency domain, and the properties of the resulting deterministic timefrequency equation clarify the nature of the nonstationary random process. We review the transformation to the time-frequency domain, and we prove the correctness of the obtained time-frequency equation.