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Izvestiya: Mathematics, 2021, Volume 85, Issue 5, Pages 852–882
DOI: https://doi.org/10.1070/IM9075 (Mi im9075) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On distributions of homogeneous and convex functions in Gaussian random variables

V. I. Bogachevab, E. D. Kosovab, S. N. Popovacb

a Lomonosov Moscow State University
b National Research University "Higher School of Economics", Moscow
c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
English version PDF (594 kB) Citations (2)
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DOI: https://doi.org/10.1070/IM9075
Abstract: We obtain broad conditions under which distributions of homogeneous functions in Gaussian and more general random variables have bounded densities or even densities of bounded variation or densities with finite Fisher information. Analogous results are obtained for convex functions. Applications to maxima of quadratic forms are given.
Keywords: distribution density, quadratic form in Gaussian random variables, distribution of a homogeneous function.
Funding agency Grant number
Russian Science Foundation 17-11-01058
Contest «Young Russian Mathematics»
This work was supported by the Russian Science Foundation, grant no. 17-11-01058, at Lomonosov Moscow State University. The second author is a winner of the “Young Russian Mathematics” contest and thanks its sponsors and jury.
Received: 22.06.2020
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2021, Volume 85, Issue 5, Pages 25–57
DOI: https://doi.org/10.4213/im9075
Bibliographic databases:
Document Type: Article
UDC: 519.21
MSC: 60E05, 60E20, 28C15, 46G12
Language: English
Original paper language: Russian
Citation: V. I. Bogachev, E. D. Kosov, S. N. Popova, “On distributions of homogeneous and convex functions in Gaussian random variables”, Izv. RAN. Ser. Mat., 85:5 (2021), 25–57; Izv. Math., 85:5 (2021), 852–882
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:31
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