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A Distributional Approach to Multiple Stochastic Integrals and Transformations of the Poisson Measure |
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| Authors: | Sergio Albeverio Nataliya V. Smorodina |
| Affiliation: | (1) IAM, University of Bonn, D 53115 Bonn, Germany;(2) BiBoS Research Centre, D 33615 Bielefeld, Germany;(3) IZKS, D 53115 Bonn, Germany;(4) CERFIM, Locarno, Switzerland;(5) Acc. Arch., USI, , Switzerland;(6) St.-Petersburg State University, St.-Petersburg, Russia |
| 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. |
| Keywords: | Poisson random measures multiple stochastic integrals absolute continuity Radon– Nikodym derivative |
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