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The asymptotic distribution of the range and other functions of partial sums of stationary processes
Author(s) -
Siddiqui M. M.
Publication year - 1976
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr012i006p01271
Subject(s) - autoregressive model , mathematics , independent and identically distributed random variables , limit (mathematics) , range (aeronautics) , central limit theorem , class (philosophy) , markov chain , stationary distribution , distribution (mathematics) , combinatorics , mathematical analysis , statistics , random variable , computer science , materials science , artificial intelligence , composite material
Let ℰ n , n = 1, 2, ⋯ , be the net input in a reservoir during the n th period of time, and set S 0 = 0, S n = ℰ 1 + … + ℰ n , = 1, 2, ⋯ . Many quantities of interest, such as range, first‐passage times, and duration of deficit period, are functions of the partial sums S n . In this paper it is pointed out that the functional central limit theorem, which has been previously used to obtain asymptotic results for independent and identically distributed ℰ n , can be applied to a class of stationary sequences as well. To this class belong m ‐dependent, Markov, autoregressive, and autoregressive‐moving average types of stationary processes.