Canonical Lévy process and Malliavin calculus
By J. L. Solé, Frederic Utzet, J. Vives. 2007
103 citations recorded by the source corpus.
A suitable canonical Levy process is constructed in order to study a Malliavin calculus based on a chaotic representation property of Levy processes proved by Ito using multiple two-parameter integrals. In this setup, the two-parameter derivative Dt,x is studied, depending on whether x=0 or x[not equal to]0; in the first case, we prove a chain rule; in the second case, a formula by trajectories.
Subfields: Economics and Econometrics, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a9d07b44621bd1ef35dad1d58130457c0b44283e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Economics and Econometrics
In Finance
- Giovanni Peccati
- E. Petrou
- Matthias Schulte
- Murad S. Taqqu
- Frederic Utzet
- J. L. Sol'e
- Ivan Nourdin
- David Nualart
In Mathematical Physics
- E. Petrou
- Giovanni Peccati
- Murad S. Taqqu
- Ivan Nourdin
- David Nualart
- Matthias Schulte
- Michel Ledoux
- Gesine Reinert
Citations in the corpus
- Malliavin Calculus in Lévy spaces and Applications to Finance. (2008, methodology): “In our case we adopt the definition of directional derivative first introduced in Nualart and Vives [14] for pure jump processes and then used in Léon et al. [11] and Solé et al.[16].”
- Stein’s method and Normal approximation of Poisson functionals (2008, methodology): “6, we could alternatively use the definition of the Malliavin derivative introduced in [30], that is, D(t,x)F = F(t,x) − F x , a.”