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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 298, Pages 134–149 (Mi znsl1167)  
On random broken lines weakly converging to fractional Ornstein–Uhlenbeck process

A. V. Liber, O. V. Rusakov

Saint-Petersburg State University
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Abstract: The behavior of sequences of continuous broken lines corresponding to sums of stationary sequences is studied. Conditions of weak convergence of distributions of these broken lines to Gaussian processes of Ornstein–Uhlenbeck type and fractional Brownian movement type are established.
Received: 10.09.2003
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 128, Issue 1, Pages 2569–2577
DOI: https://doi.org/10.1007/s10958-005-0204-1
Bibliographic databases:
UDC: 519.2
Language: Russian
Citation: A. V. Liber, O. V. Rusakov, “On random broken lines weakly converging to fractional Ornstein–Uhlenbeck process”, Probability and statistics. Part 6, Zap. Nauchn. Sem. POMI, 298, POMI, St. Petersburg, 2003, 134–149; J. Math. Sci. (N. Y.), 128:1 (2005), 2569–2577
Citation in format AMSBIB
\Bibitem{LibRus03}
\by A.~V.~Liber, O.~V.~Rusakov
\paper On random broken lines weakly converging to fractional Ornstein--Uhlenbeck process
\inbook Probability and statistics. Part~6
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 298
\pages 134--149
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1167}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2038868}
\zmath{https://zbmath.org/?q=an:1074.60028}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 128
\issue 1
\pages 2569--2577
\crossref{https://doi.org/10.1007/s10958-005-0204-1}
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