Mixing of Poisson random measures under interacting transformations
نویسنده
چکیده
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.
منابع مشابه
Invariance of Poisson measures under random transformations
We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for adapted and anticipating Poisson stochastic integrals, and is inspired by the method of Üstünel and Zakai, Probab. Theory Relat. Fields 103, 1995, on the Wiener ...
متن کاملEntropy of infinite systems and transformations
The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...
متن کاملThe Fourier-mehler Transform and Generalized Dilations of Gaussian and Poisson Measures
We deene a family of random dilations of the Wiener and Poisson measures, and show that they can be represented as generalised Fourier-Mehler transforms. These (not quasi invariant) transformations include transforms given e.g. by time changes on Brownian motion. The generators of one-parameter families of such transformations are computed, and the Poisson case is also considered.
متن کاملRAPPORT Central limit theorem for a class of random measures associated with germ - grain models
The paper introduces a family of stationary random measures in R d generated by so-called germ-grain models. The germ-grain model is deened as the union of i.i.d. compact random sets (grains) shifted by points (germs) of a point process. This model gives rise to random measures deened by the sum of contributions of non-overlapping parts of the individual grains. The corresponding moment measure...
متن کاملMore about measures and Jacobians of singular random matrices
In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.
متن کامل