Denseness of certain smooth Lévy functionals in D1;2

• Autorzy: Geiss C. , Laukkarinen E.
• Języki publikacji: EN

Abstrakty

EN

The Malliavin derivative for a Lévy process (X_t) can be defined on the space D_1;2 using a chaos expansion or in the case of a pure jump process also via an increment quotient operator. In this paper we define the Malliavin derivative operator D on the class S of smooth random variables f(X_t1 ; : : : ;X_tn); where f is a smooth function with compact support. We show that the closure of L₂(P) ⊇ S D→ L₂(m⊗P) yields to the space D_1;2: As an application we conclude that Lipschitz functions operate on D_1;2:

Słowa kluczowe

EN

Malliavin calculus; Lévy processes

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2011
• Tom: Vol. 31, Fasc. 1
• Strony: 1--15
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Geiss C.

• Department of Mathematics, University of Innsbruck, Innsbruck, Austria

autor

Laukkarinen E.

• Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, Finland

Bibliografia

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