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Teoriya Veroyatnostei i ee Primeneniya, 2024, Volume 69, Issue 4, Pages 712–728
DOI: https://doi.org/10.4213/tvp5741 (Mi tvp5741) 		 
Spontaneously started signals with white noise

P. A. Yaskov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/tvp5741
Abstract: We give a complete description of the conditions for equivalency of the distribution of Brownian motion with randomly started drift of the square root type to the Wiener measure. This problem is closely related to the theory of Gaussian multiplicative chaos (GMC). We develop a new elementary method to prove the existence of the density of the corresponding distribution, which, in fact, is related to one-dimensional GMC in the subcritical regime.
Keywords: Brownian motion, Girsanov theorem, Cameron–Martin theorem, Gaussian multiplicative chaos.
Funding agency Grant number
Russian Science Foundation 24-71-10109
Received: 16.08.2024
Published: 25.10.2024
English version:
Theory of Probability and its Applications, 2025, Volume 69, Issue 4, Pages 565–578
DOI: https://doi.org/10.1137/S0040585X97T992136
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: P. A. Yaskov, “Spontaneously started signals with white noise”, Teor. Veroyatnost. i Primenen., 69:4 (2024), 712–728; Theory Probab. Appl., 69:4 (2025), 565–578
Citation in format AMSBIB
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\by P.~A.~Yaskov
\paper Spontaneously started signals with white noise
\jour Teor. Veroyatnost. i Primenen.
\yr 2024
\vol 69
\issue 4
\pages 712--728
\mathnet{http://mi.mathnet.ru/tvp5741}
\crossref{https://doi.org/10.4213/tvp5741}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4914726}
\transl
\jour Theory Probab. Appl.
\yr 2025
\vol 69
\issue 4
\pages 565--578
\crossref{https://doi.org/10.1137/S0040585X97T992136}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-86000123208}
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  • https://www.mathnet.ru/eng/tvp/v69/i4/p712
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