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Teor. Veroyatnost. i Primenen., 2021, Volume 66, Issue 1, Pages 73–93 (Mi tvp5410)  

An approximation of the Wiener process local time by functionals of random walks.

I. A. Ibragimovab, N. V. Smorodinaab*, M. M. Faddeevab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University

Abstract: We consider a family of compound Poisson processes generated by sums of i.i.d. random variables that weakly converges to the Wiener process. We prove convergence in distribution of some functionals of these processes to the Brownian local time.

Keywords: Random processes, limit theorems, local time.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00657

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tvp5410

Full text: PDF file (448 kB)
First page: PDF file
References: PDF file   HTML file

MSC: 60H05, 60G57
Received: 18.04.2020

Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “An approximation of the Wiener process local time by functionals of random walks.”, Teor. Veroyatnost. i Primenen., 66:1 (2021), 73–93

Citation in format AMSBIB
\Bibitem{IbrSmoFad21}
\by I.~A.~Ibragimov, N.~V.~Smorodina, M.~M.~Faddeev
\paper An approximation of the Wiener process local time by functionals of
random walks.
\jour Teor. Veroyatnost. i Primenen.
\yr 2021
\vol 66
\issue 1
\pages 73--93
\mathnet{http://mi.mathnet.ru/tvp5410}
\crossref{https://doi.org/10.4213/tvp5410}


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