Abstract
We study a class of ‘nonpoissonian’ transformations of the configuration space and the corresponding transformations of the Poisson measure. For some class of Poisson measures we find conditions which are sufficient for the transformed measure (which in general is nonpoissonian) to be absolutely continuous with respect to the initial Poisson measure and get the expression for the corresponding Radon–Nikodym derivative. To solve this problem we use a distributional approach to Poisson multiple stochastic integrals.
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Albeverio, S., Smorodina, N.V. A Distributional Approach to Multiple Stochastic Integrals and Transformations of the Poisson Measure. Acta Appl Math 94, 1–19 (2006). https://doi.org/10.1007/s10440-006-9062-1
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DOI: https://doi.org/10.1007/s10440-006-9062-1