Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 501, Pages 38–41
DOI: https://doi.org/10.31857/S2686954321060072 (Mi danma219) 		 
This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

On a family of complex-valued stochastic processes

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

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b Saint Petersburg State University, St. Petersburg, Russia
Full-text PDF (186 kB) Citations (3)
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DOI: https://doi.org/10.31857/S2686954321060072
Abstract: We introduce a family $r_\lambda$, $\lambda\in\mathbb C$ of complex-valued stochastic processes making it possible to construct a probabilistic representation for the resolvent of the operator $-\frac12\frac{d^2}{dx^2}$. For $\lambda=0$ the process $r_\lambda$ is real-valued and coincides with the Brownian local time process.
Keywords: random processes, local time.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00657
Faddeev acknowledges the support of the Russian Foundation for Basic Research, project no. 19-01-00657.
Received: 14.08.2021
Revised: 14.08.2021
Accepted: 08.09.2021
English version:
Doklady Mathematics, 2021, Volume 104, Issue 3, Pages 347–350
DOI: https://doi.org/10.1134/S1064562421060077
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “On a family of complex-valued stochastic processes”, Dokl. RAN. Math. Inf. Proc. Upr., 501 (2021), 38–41; Dokl. Math., 104:3 (2021), 347–350
Citation in format AMSBIB
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\paper On a family of complex-valued stochastic processes
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\vol 501
\pages 38--41
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\crossref{https://doi.org/10.31857/S2686954321060072}
\zmath{https://zbmath.org/?q=an:7503276}
\elib{https://elibrary.ru/item.asp?id=47371415}
\transl
\jour Dokl. Math.
\yr 2021
\vol 104
\issue 3
\pages 347--350
\crossref{https://doi.org/10.1134/S1064562421060077}
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    • This publication is cited in the following 3 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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