Probability Theory
Geometrization of Monte-Carlo numerical analysis of an elliptic operator: strong approximation
Comptes Rendus. Mathématique, Volume 338 (2004) no. 6, pp. 481-486.

A one-step scheme is constructed, which, as the Milstein scheme, has the strong approximation property of order 1; in contrast to the Milstein scheme, our scheme does not involve the simulation of iterated Itô integrals of second order.

On propose un schéma à un pas, qui, comme le schéma de Milstein, possède la propriété d'approximation forte à l'ordre 1 ; contrairement au schéma de Milstein, notre schéma ne nécessite pas la simulation d'intégrales itérées de Itô du second degré.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.01.007
Cruzeiro, Ana Bela 1; Malliavin, Paul 2; Thalmaier, Anton 3

1 Grupo de Fı́sica-Matemática UL and Dep. Matemática IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
2 10, rue Saint Louis en l'Isle, 75004 Paris, France
3 Département de mathématiques, Université de Poitiers, téléport 2, BP 30179, 86962 Futuroscope Chasseneuil, France
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Cruzeiro, Ana Bela; Malliavin, Paul; Thalmaier, Anton. Geometrization of Monte-Carlo numerical analysis of an elliptic operator: strong approximation. Comptes Rendus. Mathématique, Volume 338 (2004) no. 6, pp. 481-486. doi : 10.1016/j.crma.2004.01.007. http://www.numdam.org/articles/10.1016/j.crma.2004.01.007/

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