Abstract
Let H be an infinite dimensional separable Hilbert space and μ = N Q a non degenerate Gaussian measure. For any ϕ ∈ ℰ(H) (the space of all exponential functions, see Section 3.2) we define the Malliavin derivative of ϕ setting
where D represents the gradient. The factor Q 1/2 in front of the gradient, has far reaching consequences that we shall explain later (see Remark 3.2 and Chapter 11).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Scuola Normale Superiore Pisa
About this chapter
Cite this chapter
Da Prato, G. (2014). The Malliavin derivative. In: Introduction to Stochastic Analysis and Malliavin Calculus. Publications of the Scuola Normale Superiore, vol 13. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-499-1_3
Download citation
DOI: https://doi.org/10.1007/978-88-7642-499-1_3
Publisher Name: Edizioni della Normale, Pisa
Print ISBN: 978-88-7642-497-7
Online ISBN: 978-88-7642-499-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)