A Distributional Approach to Multiple Stochastic Integrals and Transformations of the Poisson Measure, II

Autores: Sergio A. Albeverio, Nataliya V. Smorodina
Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 102, Nº. 2-3, 2008, págs. 319-343
Idioma: inglés
DOI: 10.1007/s10440-008-9223-5
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Resumen
- We study a class of �nonpoissonian� transformations of the configuration space (over a space of the form G=S×R, where S is a complete separable metric space) and the corresponding transformations of the Poisson measure. For the Poisson measures of the Lévy-Khinchin type we find conditions which are sufficient to ensure that the transformed measure (which in general is nonpoissonian) is absolutely continuous with respect to the initial Poisson measure and derive an expression for the corresponding Radon-Nikodym derivative. To this end we use a distributional approach to Poisson multiple stochastic integrals. This is the second of a series of papers, as compared to the first part the space G is different and the intensity measure is more general, allowing a stronger singularity at the origin.