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Cut-off phenomenon for Ornstein-Uhlenbeck processes driven by Lévy processes
- Source :
- Electron. J. Probab.
- Publication Year :
- 2020
-
Abstract
- In this paper, we study the cut-off phenomenon under the total variation distance of $d$-dimensional Ornstein-Uhlenbeck processes which are driven by L\'evy processes. That is to say, under the total variation distance, there is an abrupt convergence of the aforementioned process to its equilibrium, i.e. limiting distribution. Despite that the limiting distribution is not explicit, its distributional properties allow us to deduce that a profile function always exists in the reversible cases and it may exist in the non-reversible cases under suitable conditions on the limiting distribution. The cut-off phenomena for the average and superposition processes are also determined.<br />Comment: 34 pages. Electronic Journal of Probability 2020
- Subjects :
- Statistics and Probability
Random dynamical systems
HITTING TIMES
FOS: Physical sciences
Asymptotic distribution
Ornstein-Uhlenbeck processes
Dynamical Systems (math.DS)
01 natural sciences
Lévy process
114 Physical sciences
ABRUPT CONVERGENCE
010104 statistics & probability
Total variation
Superposition principle
Cut-off phenomenon
60E07
Phenomenon
Convergence (routing)
FOS: Mathematics
111 Mathematics
EQUATION
DISTRIBUTIONS
Statistical physics
Mathematics - Dynamical Systems
0101 mathematics
112 Statistics and probability
Mathematical Physics
Mathematics
60G60
37A25
Levy processes
total variation distance
Probability (math.PR)
010102 general mathematics
Ornstein–Uhlenbeck process
Mathematical Physics (math-ph)
Function (mathematics)
PERTURBATIONS
Lévy processes
Statistics, Probability and Uncertainty
60G10
Mathematics - Probability
60G51, 60G60, 60G10, 60E07, 37A25
60G51
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Electron. J. Probab.
- Accession number :
- edsair.doi.dedup.....6dfb390cda0b2b7e12607e8fc0b0af2f