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 first continuous derivative, i.e., C^1. We show that known cubature 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 9.

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. Kristian Bredies, Christian Clason, Karl Kunisch, Gregory Winckel. Control and Optimization with PDE Constraints, Springer Basel, pp.159-172, 2013, International Series of Numerical Mathematics, 978-3-0348-0630-5. ⟨10.1007/978-3-0348-0631-2_9⟩. ⟨hal-00660875v2⟩