An Extension of the Ocone–Haussmann–Clark Formula for the Compensated Poisson Processes

The Sobolev-type spaces $D_{p,1,\alpha }^{CP}$ ($1\le p\le2$) are defined for the compensated Poisson process, and the stochastic integral representation (analogous to the Ocone–Haussmann–Clark formula) is derived for the functionals from these spaces. The formula is given for the computation of the predictable projections of the stochastic derivatives of the above-mentioned functionals.