Regularity of the Laws of Shot Noise Series and of Related Processes

Jean-Christophe Breton ()
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Jean-Christophe Breton: Université de La Rochelle

Journal of Theoretical Probability, 2010, vol. 23, issue 1, 21-38

Abstract: Abstract We investigate the regularity of shot noise series and of Poisson integrals. We give conditions for the absolute continuity of their law with respect to the Lebesgue measure and for their continuity in total-variation norm. In particular, the case of truncated series in addressed. Our method relies on a disintegration of the probability space based on a mere conditioning by the first jumps of the underlying Poisson process.

Keywords: Absolute continuity; Convergence in variation; Disintegration of probability space; Poisson integrals; Shot noise series; 60B10; 60F99; 60H05; 60H10 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0255-1

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