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Keywords:
drift; Wiener process; partial sums
drift; Wiener process; partial sums
Summary:
If a stochastic process can be approximated with a Wiener process with positive drift, then its maximum also can be approximated with a Wiener process with positive drift.
References:
[1] Chow Y. S., Hsiung A. C.: Limiting behavior of $ \max _{j \le n} S_j/j^\alpha $ and the first passage times in a random walk with positive drift. Bull. Inst. Math. Acad. Sinica 4 (1976), 35–44 MR 0407948
[2] Chow Y. S., Hsiung A. C., Yu K. F.: Limit theorems for a positively drifting process and its related first passage times. Bull. Inst. Math. Acad. Sinica 8 (1980), 141–172 MR 0595527 | Zbl 0441.60075
[3] Komlós J., Major, P., Tusnády G.: An approximation of partial sums of independent R. V.’s and the sample D.F.I. Z. Wahrschein. Verw. Gebiete 32 (1975), 111–131 DOI 10.1007/BF00533093 | MR 0375412
[4] Komlós J., Major, P., Tusnády G.: An approximation of partial sums of independent R. V.’s and the sample D.F.I. Z. Wahrsch. Verw. Gebiete 34 (1976), 33–58 DOI 10.1007/BF00532688 | MR 0402883
[5] Major P.: The approximation of partial sums of independent R. V.’s. Z. Wahrsch. Verw. Gebiete 35 (1976), 213–220 DOI 10.1007/BF00532673 | MR 0415743 | Zbl 0338.60031
[6] Teicher H.: A classical limit theorem without invariance or reflection. Ann. Probab. 1 (1973), 702–704 DOI 10.1214/aop/1176996897 | MR 0350818 | Zbl 0262.60013
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