Distribution-valued iterated gradient
and chaotic decompositions of
Poisson jump times functionals.
| Nicolas Privault |
| Université de la Rochelle |
| Avenue Michel Crépeau |
| 17042 La Rochelle Cedex 1 |
| France |
Abstract:
We define a class of distributions on Poisson space
which allows to iterate
a modification of the gradient of [1].
As an application we obtain,
with relatively short calculations,
a formula for the chaos expansion of functionals of jump times of
the Poisson process.
Key words:
Poisson process, stochastic analysis,
chaotic decompositions.
Mathematics Subject Classification:
60J75, 60H05.
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