TY - CHAP
T1 - Local Gradients on the Poisson Space
AU - Privault, Nicolas
PY - 2009
Y1 - 2009
N2 - We study a class of local gradient operators on Poisson space that have the derivation property. This allows us to give another example of a gradient operator that satisfies the hypotheses of Chapter 3, this time for a discontinuous process. In particular we obtain an anticipative extension of the compensated Poisson stochastic integral and other expressions for the Clark predictable representation formula. The fact that the gradient operator satisfies the chain rule of derivation has important consequences for deviation inequalities, computation of chaos expansions, characterizations of Poisson measures, and sensitivity analysis. It also leads to the definition of an infinite dimensional geometry under Poisson measures.
AB - We study a class of local gradient operators on Poisson space that have the derivation property. This allows us to give another example of a gradient operator that satisfies the hypotheses of Chapter 3, this time for a discontinuous process. In particular we obtain an anticipative extension of the compensated Poisson stochastic integral and other expressions for the Clark predictable representation formula. The fact that the gradient operator satisfies the chain rule of derivation has important consequences for deviation inequalities, computation of chaos expansions, characterizations of Poisson measures, and sensitivity analysis. It also leads to the definition of an infinite dimensional geometry under Poisson measures.
U2 - 10.1007/978-3-642-02380-4_8
DO - 10.1007/978-3-642-02380-4_8
M3 - Chapter in research book/monograph/textbook (Author)
SN - 9783642023798
T3 - Lecture Notes in Mathematics
SP - 247
EP - 280
BT - Stochastic Analysis in Discrete and Continuous Settings
PB - Springer Berlin Heidelberg
ER -