Summary
The well-known and widely used Laplace resp. probability generating functionals are characterized by properties of positive definiteness and continuity. The methods applied come from Harmonic Analysis on semigroups, and allow also intrinsic characterizations for the transforms of infinitely divisible random measures and point processes.
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Ressel, P., Schmidtchen, W. A new characterization of Laplace functionals and probability generating functionals. Probab. Th. Rel. Fields 88, 195–213 (1991). https://doi.org/10.1007/BF01212559
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DOI: https://doi.org/10.1007/BF01212559
Keywords
- Stochastic Process
- Probability Theory
- Harmonic Analysis
- Mathematical Biology
- Point Process