Iguchi, Y;
Jasra, A;
Maama, M;
Beskos, A;
(2025)
Antithetic Multilevel Methods for Elliptic and Hypoelliptic Diffusions with Applications.
SIAM/ASA Journal on Uncertainty Quantification
, 13
(2)
, Article 2. 10.1137/24M1695178.
Preview |
PDF
M169517.pdf - Accepted Version Download (498kB) | Preview |
Abstract
We present a new antithetic multilevel Monte Carlo (MLMC) method for the estimation of expectations with respect to laws of diffusion processes that can be elliptic or hypoelliptic. In particular, we consider the case where one has to resort to time discretization of the diffusion and numerical simulation of such schemes. Inspired by recent works, we introduce a new MLMC estimator of expectations, which does not require any Lévy area simulation and has a strong error of order 2 and a weak error of order 2. We then show how this approach can be used in the context of the filtering problem associated with partially observed diffusions with discrete time observations. We illustrate that in numerical simulations our new approaches provide efficiency gains for several problems, particularly when the diffusion process is hypoelliptic, relative to some existing methods.
| Type: | Article |
|---|---|
| Title: | Antithetic Multilevel Methods for Elliptic and Hypoelliptic Diffusions with Applications |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/24M1695178 |
| Publisher version: | https://doi.org/10.1137/24m1695178 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Interdisciplinary Applications, Physics, Mathematical, Mathematics, Physics, stochastic differential equations, multilevel Monte Carlo, filtering, PARTICLE FILTERS |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10211276 |
Archive Staff Only
 |
View Item |
