Wavelets and stochastic processes

Wavelets are known to have intimate connections to several other parts of m athematics, notably phase-space analysis of signal processing, reproducing kernel Hilbert spaces, coherent states in quantum mechanics, spline approxi mation theory, windowed Fourier transforms, and filter banks. Here, we esta blish and survey a new connection, namely to stochastic processes. Key to t his link are the Kolmogorov systems of ergodic theory. (C) 1999 IMACS/Elsev ier Science B.V. All rights reserved.