Chain rules and p-variation

• Autorzy: R. Norvaiša
• Języki publikacji: EN

Abstrakty

EN

The main result is a Young-Stieltjes integral representation of the composition ϕ ∘ f of two functions f and ϕ such that for some α ∈ (0,1], ϕ has a derivative satisfying a Lipschitz condition of order α, and f has bounded p-variation for some p < 1 + α. If given α ∈ (0,1], the p-variation of f is bounded for some p < 2 + α, and ϕ has a second derivative satisfying a Lipschitz condition of order α, then a similar result holds with the Young-Stieltjes integral replaced by its extension.

Kategorie tematyczne

• 26A45: Functions of bounded variation, generalizations
• 26A42: Integrals of Riemann, Stieltjes and Lebesgue type
• 60H05: Stochastic integrals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 149
• Numer: 3
• Strony: 197-238

Daty

wydano

2002

Twórcy

autor

R. Norvaiša

• Institute of Mathematics and Informatics, Akademijos 4, Vilnius 2600, Lithuania

Identyfikatory

DOI

10.4064/sm149-3-1