### Abstract

We study limiting properties of a random walk on the plane, when we have a square lattice on the upper half-plane and a comb structure on the lower half-plane, i.e., horizontal lines below the x-axis are removed. We give strong approximations for the components with random time changed Wiener processes. As consequences, limiting distributions and some laws of the iterated logarithm are presented. Finally, a formula is given for the probability that the random walk returns to the origin in 2N steps.

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

Pages (from-to) | 29-44 |

Number of pages | 16 |

Journal | Annales Mathematicae et Informaticae |

Volume | 39 |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- Anisotropic random walk
- Laws of the iterated logarithm
- Local time
- Strong approximation
- Wiener process

### ASJC Scopus subject areas

- Mathematics(all)
- Computer Science(all)

### Cite this

*Annales Mathematicae et Informaticae*,

*39*, 29-44.

**Random walk on half-plane half-comb structure.** / Csáki, E.; Csörgo, Miklós; Földes, Antónia; Révész, Pál.

Research output: Contribution to journal › Article

*Annales Mathematicae et Informaticae*, vol. 39, pp. 29-44.

}

TY - JOUR

T1 - Random walk on half-plane half-comb structure

AU - Csáki, E.

AU - Csörgo, Miklós

AU - Földes, Antónia

AU - Révész, Pál

PY - 2012

Y1 - 2012

N2 - We study limiting properties of a random walk on the plane, when we have a square lattice on the upper half-plane and a comb structure on the lower half-plane, i.e., horizontal lines below the x-axis are removed. We give strong approximations for the components with random time changed Wiener processes. As consequences, limiting distributions and some laws of the iterated logarithm are presented. Finally, a formula is given for the probability that the random walk returns to the origin in 2N steps.

AB - We study limiting properties of a random walk on the plane, when we have a square lattice on the upper half-plane and a comb structure on the lower half-plane, i.e., horizontal lines below the x-axis are removed. We give strong approximations for the components with random time changed Wiener processes. As consequences, limiting distributions and some laws of the iterated logarithm are presented. Finally, a formula is given for the probability that the random walk returns to the origin in 2N steps.

KW - Anisotropic random walk

KW - Laws of the iterated logarithm

KW - Local time

KW - Strong approximation

KW - Wiener process

UR - http://www.scopus.com/inward/record.url?scp=84864111013&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864111013&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84864111013

VL - 39

SP - 29

EP - 44

JO - Annales Mathematicae et Informaticae

JF - Annales Mathematicae et Informaticae

SN - 1787-5021

ER -