Wavelets and stochastic theory: Past and future

Abstract

In the paper, authors report on the interdisciplinary and extremely complex link between wavelets and stochastic processes. An insight into the history of wavelets has been provided presenting the fundamental conception of wavelets, as well as wavelet theory that emerged from stochastic processes. The multiresolution analysis corresponds to the Kolmogorov system which is a regular stationary stochastic process. It presents a significant link to the measurement problem in terms of positional notation which the wavelet domain hidden Markov model should be derived from. The optimal representation arises to be an issue requiring further elaboration extended to the general measurement and wavelet frames.