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 |
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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