2008/05/30 by Christel Geiß, Geiss, Christel, Eija Laukkarinen +1
Economics, Econometrics and Finance · Mathematics · #60G51 #60H07 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.0805.4704
openalex publication_date 2008/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Malliavin derivative for a Lévy process (Xt) can be defined on the space \DD1,2 using a chaos expansion or in the case of a pure jump process also via an increment quotient operator \citesole-utzet-vives. In this paper we define the Malliavin derivative operator \D on the class S of smooth random variables f(Xt1, ..., Xtn), where f is a smooth function with compact support. We show that the closure of L2(\Om) ⊇ S \stackrel\D→ L2(\m⊗ \mass) yields to the space \DD1,2. As an application we conclude that Lipschitz functions map from \DD1,2 into \DD1,2.