## Abstract

We consider a family of Ornstein–Uhlenbeck processes. Under

some suitable assumptions on the behaviour of the drift and diffusion coefficients, we prove profile cut-off phenomenon with respect to the total variation distance in the sense of the definition given by Barrera and Ycart [ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 445–458]. We compute explicitly the

cut-off time, the window time, and the profile function. Moreover, we prove

that the average process satisfies a profile cut-off phenomenon with respect

to the total variation distance. Also, a sample of N Ornstein–Uhlenbeck processes

has a window cut-off with respect to the total variation distance in the

sense of the definition given by Barrera and Ycart [ALEA Lat. Am. J. Probab.

Math. Stat. 11 (2014) 445–458]. The cut-off time and the cut-off window for

the average process and for the sampling process are the same.

some suitable assumptions on the behaviour of the drift and diffusion coefficients, we prove profile cut-off phenomenon with respect to the total variation distance in the sense of the definition given by Barrera and Ycart [ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 445–458]. We compute explicitly the

cut-off time, the window time, and the profile function. Moreover, we prove

that the average process satisfies a profile cut-off phenomenon with respect

to the total variation distance. Also, a sample of N Ornstein–Uhlenbeck processes

has a window cut-off with respect to the total variation distance in the

sense of the definition given by Barrera and Ycart [ALEA Lat. Am. J. Probab.

Math. Stat. 11 (2014) 445–458]. The cut-off time and the cut-off window for

the average process and for the sampling process are the same.

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

Journal | Brazilian Journal of Probability and Statistics |

Volume | 32 |

Issue number | 1 |

Pages (from-to) | 188-199 |

Number of pages | 12 |

ISSN | 0103-0752 |

DOIs | |

Publication status | Published - 2018 |

MoE publication type | A1 Journal article-refereed |

## Fields of Science

- 112 Statistics and probability
- Cut-off phenomenon
- Total variation distance
- Ornstein–Uhlenbeck processes