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Teoriya Veroyatnostei i ee Primeneniya, 2023, Volume 68, Issue 3, Pages 544–564
DOI: https://doi.org/10.4213/tvp5555 (Mi tvp5555) 		 
On a family of random operators

I. A. Ibragimovab, N. V. Smorodinaab, M. M. Faddeevb

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University
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DOI: https://doi.org/10.4213/tvp5555
Abstract: Random operators arising in the construction of probabilistic representation of the resolvent of the operator $-\frac{1}{2}\,\frac{d}{dx}\bigl(b^2(x)\frac{d}{dx}\bigr)$ are considered and shown to be integral with probability $1$. Properties of their kernels are investigated.
Keywords: random processes, local time, random operator.
Funding agency Grant number
Russian Science Foundation 22-21-00016
Received: 05.02.2022
Revised: 11.02.2023
English version:
Theory of Probability and its Applications, 2023, Volume 68, Issue 3, Pages 440–456
DOI: https://doi.org/10.1137/S0040585X97T991556
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “On a family of random operators”, Teor. Veroyatnost. i Primenen., 68:3 (2023), 544–564; Theory Probab. Appl., 68:3 (2023), 440–456
Citation in format AMSBIB
\Bibitem{IbrSmoFad23}
\by I.~A.~Ibragimov, N.~V.~Smorodina, M.~M.~Faddeev
\paper On a family of random operators
\jour Teor. Veroyatnost. i Primenen.
\yr 2023
\vol 68
\issue 3
\pages 544--564
\mathnet{http://mi.mathnet.ru/tvp5555}
\crossref{https://doi.org/10.4213/tvp5555}
\transl
\jour Theory Probab. Appl.
\yr 2023
\vol 68
\issue 3
\pages 440--456
\crossref{https://doi.org/10.1137/S0040585X97T991556}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85179350701}
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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