Abstract
Let (X n) denote an independent and identically distributed random sequence. Let S n = σ; k = 1 nX k and M n = maxX 1,.., X n be its partial sum and maximum. Suppose that some of the random variables of X 1, X 2,.. can be observed and denote by M n the maximum of observed random variables from the set X 1,.., X n. In this paper, we consider the joint limiting distribution of (M n, M n, S n) and the almost sure central limit theorems related to the random vector (M n, M n, S n). Furthermore, we extend related results to weakly dependent stationary Gaussian sequences. © 2012 World Scientific Publishing Company.
Original language | English |
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Article number | 1150026 |
Journal | Stochastics and Dynamics |
Volume | 12 |
Issue number | 3 |
DOIs | |
Publication status | Published - Sept 2012 |
Keywords
- Almost sure central limit theorem
- joint limiting distribution
- maximum
- missing observations
- partial sum
- stationary Gaussian sequence