Wavelets and stochastic theory: Past and future
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2023
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Elsevier Ltd.
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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 dynamicsSource:
Chaos, Solitons & Fractals, 2023, 173, 113724Publisher:
- Elsevier
Funding / projects:
- Ministry of Science, Technological Development and Innovation of the Republic of Serbia, institutional funding - 200053 (University of Belgrade, Institute for Multidisciplinary Research) (RS-MESTD-inst-2020-200053)
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Institut za multidisciplinarna istraživanjaTY - JOUR AU - Milovanović, Miloš AU - Tomić, Bojan AU - saulig, nicoletta PY - 2023 UR - http://rimsi.imsi.bg.ac.rs/handle/123456789/2860 AB - 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. PB - Elsevier T2 - Chaos, Solitons & Fractals T1 - Wavelets and stochastic theory: Past and future IS - 113724 VL - 173 DO - 10.1016/j.chaos.2023.113724 ER -
@article{ author = "Milovanović, Miloš and Tomić, Bojan and saulig, nicoletta", year = "2023", 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.", publisher = "Elsevier", journal = "Chaos, Solitons & Fractals", title = "Wavelets and stochastic theory: Past and future", number = "113724", volume = "173", doi = "10.1016/j.chaos.2023.113724" }
Milovanović, M., Tomić, B.,& saulig, n.. (2023). Wavelets and stochastic theory: Past and future. in Chaos, Solitons & Fractals Elsevier., 173(113724). https://doi.org/10.1016/j.chaos.2023.113724
Milovanović M, Tomić B, saulig N. Wavelets and stochastic theory: Past and future. in Chaos, Solitons & Fractals. 2023;173(113724). doi:10.1016/j.chaos.2023.113724 .
Milovanović, Miloš, Tomić, Bojan, saulig, nicoletta, "Wavelets and stochastic theory: Past and future" in Chaos, Solitons & Fractals, 173, no. 113724 (2023), https://doi.org/10.1016/j.chaos.2023.113724 . .