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

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.

MSC: Primary 60F17; Secondary 60F15,60G52,60G50

Language: English

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