Norms of powers and a central limit theorem for complex-valued probabilities

Baishanski, Bogdan M.

doi:10.1007/978-1-4612-2236-1_29

Cited by 2 publications

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“…In the case of complex-valued probability, Baishanski (1998) For some results in this direction, see Baez-Duarte (1993) and Baishanski (1998).…”

Section: Convolutions Of Signed Measure Model and Quasi-infinitely DImentioning

confidence: 99%

“…His work stemmed from an open problem related to the complex-valued probability model which was first posed by Beurling (1938) and later quoted by Beurling and Helson (1953). It is called the problem of "Norms of powers of absolutely convergent Fourier series" and has been investigated at length in many, many papers; see Baishanski (1998) for a review. We only present the problem here and show its relationship to the DPCP distribution.…”

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confidence: 99%

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A characterization of signed discrete infinitely divisible distributions

Zhang

Kerns³

2017

Studia Scientiarum Mathematicarum Hungarica

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In this article, we give some reviews concerning negative probabilities model and quasi-infinitely divisible at the beginning. We next extend Feller's characterization of discrete infinitely divisible distributions to signed discrete infinitely divisible distributions, which are discrete pseudo compound Poisson (DPCP) distributions with connections to the Lévy-Wiener theorem. This is a special case of an open problem which is proposed by Sato (2014), Chaumont and Yor (2012). An analogous result involving characteristic functions is shown for signed integer-valued infinitely divisible distributions. We show that many distributions are DPCP by the non-zero p.g.f. property, such as the mixed Poisson distribution and fractional Poisson process. DPCP has some bizarre properties, and one is that the parameter λ in the DPCP class cannot be arbitrarily small.

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“…In the case of complex-valued probability, Baishanski (1998) For some results in this direction, see Baez-Duarte (1993) and Baishanski (1998).…”

Section: Convolutions Of Signed Measure Model and Quasi-infinitely DImentioning

confidence: 99%

mentioning

confidence: 99%