### Abstract

Consider a Wiener process {W(t),t≧0}, let M(t)=max |W(s)| and v(t) be the location of the maximum of the absolute value of {Mathematical expression} in [0, t] i.e. |W(v(t))|=M(t). We study the limit points of (α_{t}M(t),β_{t}v(t)) as t→∞ where α_{t} and β_{t} are positive, decreasing normalizing constants. Moreover, a lim inf result is proved for the length of the longest flat interval of M(t).

Original language | English |
---|---|

Pages (from-to) | 477-497 |

Number of pages | 21 |

Journal | Probability Theory and Related Fields |

Volume | 76 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1987 |

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### ASJC Scopus subject areas

- Statistics and Probability
- Analysis
- Mathematics(all)

### Cite this

*Probability Theory and Related Fields*,

*76*(4), 477-497. https://doi.org/10.1007/BF00960069

**On the maximum of a Wiener process and its location.** / Csáki, E.; Földes, A.; Révész, P.

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 76, no. 4, pp. 477-497. https://doi.org/10.1007/BF00960069

}

TY - JOUR

T1 - On the maximum of a Wiener process and its location

AU - Csáki, E.

AU - Földes, A.

AU - Révész, P.

PY - 1987/12

Y1 - 1987/12

N2 - Consider a Wiener process {W(t),t≧0}, let M(t)=max |W(s)| and v(t) be the location of the maximum of the absolute value of {Mathematical expression} in [0, t] i.e. |W(v(t))|=M(t). We study the limit points of (αtM(t),βtv(t)) as t→∞ where αt and βt are positive, decreasing normalizing constants. Moreover, a lim inf result is proved for the length of the longest flat interval of M(t).

AB - Consider a Wiener process {W(t),t≧0}, let M(t)=max |W(s)| and v(t) be the location of the maximum of the absolute value of {Mathematical expression} in [0, t] i.e. |W(v(t))|=M(t). We study the limit points of (αtM(t),βtv(t)) as t→∞ where αt and βt are positive, decreasing normalizing constants. Moreover, a lim inf result is proved for the length of the longest flat interval of M(t).

UR - http://www.scopus.com/inward/record.url?scp=0001265546&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001265546&partnerID=8YFLogxK

U2 - 10.1007/BF00960069

DO - 10.1007/BF00960069

M3 - Article

AN - SCOPUS:0001265546

VL - 76

SP - 477

EP - 497

JO - Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

JF - Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

SN - 0178-8051

IS - 4

ER -