Authors: Milovanović, Miloš 
Tomić, Bojan
Saulig, Nicoletta
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Wavelets and stochastic theory: Past and future
Journal: Chaos, Solitons & Fractals
Volume: 173
First page: 113724
Issue Date: 2023
Rank: ~M21a
ISSN: 0960-0779
DOI: 10.1016/j.chaos.2023.113724
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.
Keywords: Multiresolution analysis | Time operator | Regular stationary processes | Measurement problem | Optimal representation | Hidden Markov model | Underlying dynamics
Publisher: Elsevier

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