Clark-Ocone type formulas on spaces of test and generalized functions of Meixner white noise analysis. (English) Zbl 1265.60127

The Clark-Ocone formula, one of the basic tools of Malliavin calculus, is extended to the framework of Meixner white noise analysis, in which instead of the Gaussian measure one uses the generalized Meixner measure \(\mu\) (depending on parameters, \(\mu\) is the Gaussian measure, the Poissonian measure, the Gamma measure, etc.). Properties of integrands in Clark-Ocone-type formulas are studied.


60H40 White noise theory
60H05 Stochastic integrals
46F25 Distributions on infinite-dimensional spaces