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Theory of Stochastic Processes, 2010, Volume 16(32), Issue 1, Pages 130–138 (Mi thsp68)  
Strong invariance principle for a superposition of random processes

N. M. Zinchenko

Department of Probability Theory, Mathematical Statistics and Actuarial Mathematics, National Taras Shevchenko University of Kyiv, 64, Volodymyrs'ka, Kyiv, Ukraine
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Abstract: The strong invariance principle (SIP) is proved for a superposition of random processes $S(N(t))$ under rather general assumptions on $S(t)$ and $N(t)$. As a consequence, a number of SIP-type results are obtained for random sums and used to investigate their rate of growth and fluctuation of increments.
Keywords: Invariance principle, randomly stopped process, Lévy process, renewal process, domain of attraction, stable process, stationary sequences, risk process, rate of growth.
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Document Type: Article
MSC: Primary 60F17; Secondary 60F15,60G52,60G50
Language: English
Citation: N. M. Zinchenko, “Strong invariance principle for a superposition of random processes”, Theory Stoch. Process., 16(32):1 (2010), 130–138
Citation in format AMSBIB
\Bibitem{Zin10}
\by N.~M.~Zinchenko
\paper Strong invariance principle for a superposition of random processes
\jour Theory Stoch. Process.
\yr 2010
\vol 16(32)
\issue 1
\pages 130--138
\mathnet{http://mi.mathnet.ru/thsp68}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2779832}
\zmath{https://zbmath.org/?q=an:1224.60062}
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