Wavelets and stochastic processes Original Research Article

Wavelets are known to have intimate connections to several other parts of mathematics, notably phase-space analysis of signal processing, reproducing kernel Hilbert spaces, coherent states in quantum mechanics, spline approximation theory, windowed Fourier transforms, and filter banks. Here, we establish and survey a new connection, namely to stochastic processes. Key to this link are the Kolmogorov systems of ergodic theory.