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Annihilation and Creation Operators

  • Nicolas PrivaultEmail author
Chapter
  • 1.3k Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 1982)

Abstract

In this chapter we present a first example of a pair of gradient and diver- gence 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 multi- ple stochastic integrals with respect to a normal martingale. In the following chapters we will implement several constructions of such operators, respec- tively 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

Keywords

Creation Operator Deterministic Function Stochastic Integral Wiener Space Covariance Identity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of MathematicsCity University of Hong KongHong Kong P.R. China

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