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Coupling the Kolmogorov diffusion: maximality and efficiency considerations
- Source :
- Advances in Applied Probability; July 2016, Vol. 48 Issue: 1 p15-35, 21p
- Publication Year :
- 2016
-
Abstract
- AbstractThis is a case study concerning the rate at which probabilistic coupling occurs for nilpotent diffusions. We focus on the simplest case of Kolmogorov diffusion (Brownian motion together with its time integral or, more generally, together with a finite number of iterated time integrals). We show that in this case there can be no Markovian maximal coupling. Indeed, there can be no efficientMarkovian coupling strategy (efficient for all pairs of distinct starting values), where the notion of efficiency extends the terminology of Burdzy and Kendall (2000). Finally, at least in the classical case of a single time integral, it is not possible to choose a Markovian coupling that is optimal in the sense of simultaneously minimizing the probability of failing to couple by time tfor all positive t. In recompense for all these negative results, we exhibit a simple efficient non-Markovian coupling strategy.
Details
- Language :
- English
- ISSN :
- 00018678 and 14756064
- Volume :
- 48
- Issue :
- 1
- Database :
- Supplemental Index
- Journal :
- Advances in Applied Probability
- Publication Type :
- Periodical
- Accession number :
- ejs40846886
- Full Text :
- https://doi.org/10.1017/apr.2016.40