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Mixing of Poisson random measures under interacting transformations (1301.0672v2)
Published 4 Jan 2013 in math.PR and math.DS
Abstract: 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.