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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2004, Volume 1, Pages 47–63
(Mi semr5)
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This article is cited in 15 scientific papers (total in 15 papers)
Research papers
Convergence and convergence rate to fractional Brownian motion for weighted random sums
T. Konstantopoulosa, A. Sakhanenkob a Department of Mathematics, University of Patras
b Ugra State University
Abstract:
We consider infinite sums of weighted i.i.d. random variables, with finite variance and arbitrary distribution, and derive a necessary and sufficient conditions for the weak convergence (in function space with uniform topology) of normalized sums to fractional Brownian motion (FBM). We consider also convergence rates questions. Using the embedding suggested by the Komlós–Major–Tusnády strong approximations method, we derive (under certain conditions on the weights) estimates for the quality of the functional approximation to FBM.
Received September 25, 2004, published October 12, 2004
Citation:
T. Konstantopoulos, A. Sakhanenko, “Convergence and convergence rate to fractional Brownian motion for weighted random sums”, Sib. Èlektron. Mat. Izv., 1 (2004), 47–63
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https://www.mathnet.ru/eng/semr5 https://www.mathnet.ru/eng/semr/v1/p47
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Abstract page: | 487 | Full-text PDF : | 199 | References: | 60 |
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