Electronic Communications in Probability

Optimal linear drift for the speed of convergence of an hypoelliptic diffusion

Arnaud Guillin and Pierre Monmarché

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Abstract

Among all generalized Ornstein-Uhlenbeck processes which sample the same invariant measure and for which the same amount of randomness (a $N$-dimensional Brownian motion) is injected in the system, we prove that the asymptotic rate of convergence is maximized by a non-reversible hypoelliptic one.

Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 74, 14 pp.

Dates
Received: 25 April 2016
Accepted: 6 October 2016
First available in Project Euclid: 27 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1477600775

Digital Object Identifier
doi:10.1214/16-ECP25

Mathematical Reviews number (MathSciNet)
MR3568348

Zentralblatt MATH identifier
1354.60084

Subjects
Primary: 60J60: Diffusion processes [See also 58J65] 35K10: Second-order parabolic equations 65C05: Monte Carlo methods

Keywords
hypocoercivity Ornstein-Uhlenbeck process irreversibility optimal sampling

Rights
Creative Commons Attribution 4.0 International License.

Citation

Guillin, Arnaud; Monmarché, Pierre. Optimal linear drift for the speed of convergence of an hypoelliptic diffusion. Electron. Commun. Probab. 21 (2016), paper no. 74, 14 pp. doi:10.1214/16-ECP25. https://projecteuclid.org/euclid.ecp/1477600775


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References

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