The multiple stochastic integrals and “nonpoissonian” transformations of the gamma measure

We study the transformations of the configuration space and the corresponding transformations of the Poisson measure. For some class of Poisson measures we find conditions for the transformed measure (possible, nonpoissonian) to be absolutely continuous and get the expression for the corresponding Radon–Nikodym derivative. To solve this problem we use the Poisson analog of the multiple stochastic integral. As an example we consider the transformations of the so-called gamma measure.