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Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2018, Issue 1, Pages 43–54 (Mi vtpmk493)  

Theory of Probability and Mathematical Statistics

New characterizations of Brownian motion

D. Kh. Kazanchyan

Lomonosov Moscow State University, Moscow

Abstract: In the paper new characterizations of Brownian motion are proved. They generalize and supplement the famous Levi theorem on the characterization of the process of Brownian motion in the class of square integrable continuous martingales. The first characterization (Theorem 1) generalizes the Levi theorem. Two other characterizations (Theorems 2 and 3) are analogues of the Levi theorem, in which the continuity condition is replaced by other conditions.

Keywords: Levy theorem, process with independent increments, infinitely divisible distributions, Brownian motion, martingales.

DOI: https://doi.org/10.26456/vtpmk493

Full text: PDF file (361 kB)
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UDC: 519.2
Received: 21.10.2017
Revised: 11.02.2018

Citation: D. Kh. Kazanchyan, “New characterizations of Brownian motion”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2018, no. 1, 43–54

Citation in format AMSBIB
\Bibitem{Kaz18}
\by D.~Kh.~Kazanchyan
\paper New characterizations of Brownian motion
\jour Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.]
\yr 2018
\issue 1
\pages 43--54
\mathnet{http://mi.mathnet.ru/vtpmk493}
\crossref{https://doi.org/10.26456/vtpmk493}
\elib{https://elibrary.ru/item.asp?id=32697535}


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