Cubature on C^1 space

Gabriel Turinici (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We explore in this paper cubature formulas over the space of functions having a rst continuous derivative, i.e., C1. We show that the classical Lyons-Victoir formulas are not optimal in this case and explain what is the origin of the loss of optimality and how to construct optimal ones; to illustrate we give cubature formulas up to (including) order 4.

Mots clés: Cubature Formulae; Stochastic Analysis; Chen Series; cubature on in nite dimensional space; Cubature Wiener

Domaines: Analyse numérique [math.NA]; Economies et finances; Probabilités [math.PR]; Finance quantitative [q-fin.CP]

Gabriel Turinici. Cubature on C^1 space. 2012. ⟨hal-00660875v1⟩