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Theory of Stochastic Processes, 2017, Volume 22(38), Issue 2, Pages 8–18 (Mi thsp176)  
On some random integral operators generated by an Arratia flow

A. A. Dorogovtsev, Ia. A. Korenovska, E. V. Glinyanaya

Institute of Mathematics, National Academy of Sciences of Ukrainian, Tereshchenkivska Str. 3, Kiev 01601, Ukraine
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Abstract: We study some properties of a random integral operator in $L_2( \mathbb{R})$ whose kernel is generated by a stationary point process related to an Arratia flow. To prove that this random operator is not bounded we estimate the rate of growth of the maximal amount of clusters in Arratia flow on intervals of unit length.
Keywords: Arratia flow, strong random operator, point process, stochastic flow.
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Document Type: Article
MSC: 60H25; 60G55; 60K35
Language: English
Citation: A. A. Dorogovtsev, Ia. A. Korenovska, E. V. Glinyanaya, “On some random integral operators generated by an Arratia flow”, Theory Stoch. Process., 22(38):2 (2017), 8–18
Citation in format AMSBIB
\Bibitem{DorKorGli17}
\by A.~A.~Dorogovtsev, Ia.~A.~Korenovska, E.~V.~Glinyanaya
\paper On some random integral operators generated by an Arratia flow
\jour Theory Stoch. Process.
\yr 2017
\vol 22(38)
\issue 2
\pages 8--18
\mathnet{http://mi.mathnet.ru/thsp176}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3843521}
\zmath{https://zbmath.org/?q=an:06987421}
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