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We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical result in the case of deterministic transformations of Poisson measures. The approach relies on moment and covariance identities for Poisson stochastic integrals with random integrands. [ABSTRACT FROM PUBLISHER]

We obtain sufficient conditions for the existence of conditional densities of functionals of the Poisson process, and expressions of these densities via the Malliavin calculus on Poisson space. These results are applied to enlargement of filtrations on Poisson space with explicit examples of computations via the Clark formula which is presented as a consequence of the Itô formula and the martingale property. The gradient operators of stochastic analysis on Poisson space are classified into three families, and each type of gradient is considered separately. [ABSTRACT FROM AUTHOR]