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The substance of this paper was summarized in Part II of [22] and in [23]. For help in its elaboration, thanks are due, in chronological order, to Harold A. Thomas of Harvard for showing me, in 1963, the papers by Hurst [12, 13], to James R. Wallis of IBM for stimulating discussions during our joint study of R/S by computer simulation; to Murad Taqqu of Columbia University for assistance in further simulations supported by the National Bureau of Economic Research, for permission to quote unpublished theorems from the thesis he wrote under my supervision [35], and for stimulating discussions; and to Hirsch Lewitan of IBM for programming assistance.
Concerning the form of this paper, particular thanks are due to Ward Whitt of Yale University, who read the text as submitted in May 1974 and who has been extremely generous with time and advice. He tightened up Theorem 5 and Conjecture 5, suggested in passing the first variant in Section 13, disproved some wrong conjectures, and generally helped identify spots where further detail and/or more mathematical pedantry were required.
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Mandelbrot, B.B. Limit theorems on the self-normalized range for weakly and strongly dependent processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 31, 271–285 (1975). https://doi.org/10.1007/BF00532867
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DOI: https://doi.org/10.1007/BF00532867