### Abstract

Let ξ_{i} be i.i.d. symmetric random variables with P (ξ_{i} = 1) = frac(1, 2) and denote by S_{n} their partial sums. We derive the distribution of the difference in the position of the last and first maximum of the random walk S_{n} up to time t.

Original language | English (US) |
---|---|

Pages (from-to) | 659-668 |

Number of pages | 10 |

Journal | Journal of Statistical Planning and Inference |

Volume | 137 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2007 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics

### Cite this

*Journal of Statistical Planning and Inference*,

*137*(3), 659-668. https://doi.org/10.1016/j.jspi.2006.06.028

}

*Journal of Statistical Planning and Inference*, vol. 137, no. 3, pp. 659-668. https://doi.org/10.1016/j.jspi.2006.06.028

**On the uniqueness of the maximum of the paths of random walks.** / Denker, Manfred Heinz; Koch, Susanne.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the uniqueness of the maximum of the paths of random walks

AU - Denker, Manfred Heinz

AU - Koch, Susanne

PY - 2007/3/1

Y1 - 2007/3/1

N2 - Let ξi be i.i.d. symmetric random variables with P (ξi = 1) = frac(1, 2) and denote by Sn their partial sums. We derive the distribution of the difference in the position of the last and first maximum of the random walk Sn up to time t.

AB - Let ξi be i.i.d. symmetric random variables with P (ξi = 1) = frac(1, 2) and denote by Sn their partial sums. We derive the distribution of the difference in the position of the last and first maximum of the random walk Sn up to time t.

UR - http://www.scopus.com/inward/record.url?scp=33750516525&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750516525&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2006.06.028

DO - 10.1016/j.jspi.2006.06.028

M3 - Article

AN - SCOPUS:33750516525

VL - 137

SP - 659

EP - 668

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 3

ER -