Appel pour actions 2005 avec les Etats-Unis, la Scandinavie et Taiwan

Thématique de la collaboration (environ 10 lignes) :

 Monte Carlo (MC) simulation is one of the most widely used numerical tools in the scientific community. A relatively recent approach, the quasi-Monte Carlo (QMC) method, uses the so-called low discrepancy sequences instead of pseudorandom numbers. Its advantage is that the resulting estimates are, in general and asymptotically, more accurate than the estimates of the MC method. However, there are two major disadvantages of the QMC method which preclude its further use in scientific applications: (i) its efficiency is usually illustrated on finite and moderate dimensional problems (for a given sample size), limiting its range of applications, and (ii) although we expect QMC estimates to be more accurate, there is no practical way to assess their accuracy. To address the latter problem, hybrid-Monte Carlo methods have recently been proposed, bringing some randomness back to the deterministic algorithms of QMC, in order to establish a statistical analysis of error. The partners of this project have recently proposed a mixed method using a moderate dimension low discrepancy sequence padded with pseudorandom numbers. This tackles the first high to infinite dimensional problem, with an associated central limit theorem. Combining the two techniques allows here again to easily estimate the resulting variance. The project aims at providing a deeper theoretical analysis of the mixed method, especially when a combination with the randomization technqiues is used, and apply it to the large class telecommunication and finance problems requiring high-dimensional simulation.

The project will allow to continue the common work initiated on the mixed method. The expected results are: