Approximations for the maximum of stochastic processes with drift

István Berkes; Lajos Horváth

Kybernetika (2003)

  • Volume: 39, Issue: 3, page [299]-306
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Berkes, István, and Horváth, Lajos. "Approximations for the maximum of stochastic processes with drift." Kybernetika 39.3 (2003): [299]-306. <http://eudml.org/doc/33644>.

@article{Berkes2003,
abstract = {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.},
author = {Berkes, István, Horváth, Lajos},
journal = {Kybernetika},
keywords = {drift; Wiener process; partial sums; drift; Wiener process; partial sum},
language = {eng},
number = {3},
pages = {[299]-306},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Approximations for the maximum of stochastic processes with drift},
url = {http://eudml.org/doc/33644},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Berkes, István
AU - Horváth, Lajos
TI - Approximations for the maximum of stochastic processes with drift
JO - Kybernetika
PY - 2003
PB - Institute of Information Theory and Automation AS CR
VL - 39
IS - 3
SP - [299]
EP - 306
AB - 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.
LA - eng
KW - drift; Wiener process; partial sums; drift; Wiener process; partial sum
UR - http://eudml.org/doc/33644
ER -

References

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  1. Chow Y. S., Hsiung A. C., Limiting behavior of max j ≤ n S j / j α and the first passage times in a random walk with positive drift, Bull. Inst. Math. Acad. Sinica 4 (1976), 35–44 (1976) MR0407948
  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 (1980) Zbl0441.60075MR0595527
  3. Komlós J., Major, P., Tusnády G., 10.1007/BF00533093, V.’s and the sample D.F.I. Z. Wahrschein. Verw. Gebiete 32 (1975), 111–131 (1975) MR0375412DOI10.1007/BF00533093
  4. Komlós J., Major, P., Tusnády G., 10.1007/BF00532688, V.’s and the sample D.F.I. Z. Wahrsch. Verw. Gebiete 34 (1976), 33–58 (1976) MR0402883DOI10.1007/BF00532688
  5. Major P., 10.1007/BF00532673, V.’s. Z. Wahrsch. Verw. Gebiete 35 (1976), 213–220 (1976) Zbl0338.60031MR0415743DOI10.1007/BF00532673
  6. Teicher H., 10.1214/aop/1176996897, Ann. Probab. 1 (1973), 702–704 (1973) Zbl0262.60013MR0350818DOI10.1214/aop/1176996897

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