### 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 1 1987 |

### ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

## Fingerprint Dive into the research topics of 'On the maximum of a Wiener process and its location'. Together they form a unique fingerprint.

## Cite this

Csáki, E., Földes, A., & Révész, P. (1987). On the maximum of a Wiener process and its location.

*Probability Theory and Related Fields*,*76*(4), 477-497. https://doi.org/10.1007/BF00960069