@inbook{34ddaa09ef474404b1580c44e7d2596a,
title = "Annihilation and Creation Operators",
abstract = "In this chapter we present a first example of a pair of gradient and divergence operators satisfying the duality Assumption 3.1.1, the Clark formula Assumption 3.2.1 and the stability Assumption 3.2.10 of Section 3.1. This construction is based on annihilation and creation operators acting on multiple stochastic integrals with respect to a normal martingale. In the following chapters we will implement several constructions of such operators, respectively when the normal martingale (Mt)t∈R+ is a Brownian motion or a compensated Poisson process. Other examples of operators satisfying the above assumptions will be built in the sequel by addition of a process with vanishing adapted projection to the gradient D, such as in Section 7.7 on the Poisson space.",
author = "Nicolas Privault",
year = "2009",
doi = "10.1007/978-3-642-02380-4_5",
language = "English",
isbn = "9783642023798",
series = "Lecture Notes in Mathematics",
publisher = "Springer Berlin Heidelberg",
pages = "131--160",
booktitle = "Stochastic Analysis in Discrete and Continuous Settings",
}