Summary
In this paper we consider some properties of rotation — invariant distributions onR n, which are determined by a form of conditional moment of order α>0. In particular we prove that the Gaussian distribution is determined uniquely by its conditional moments and we investigate the related question of finiteness of exponential moments. The case of general α>0 appears to be more difficult to analyze than the case α=2, studied previously by other authors.
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Bryc, W. Remarks on properties of probability distributions determined by conditional moments. Probab. Th. Rel. Fields 78, 51–62 (1988). https://doi.org/10.1007/BF00718034
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DOI: https://doi.org/10.1007/BF00718034
Keywords
- Gaussian Distribution
- Probability Distribution
- Stochastic Process
- Probability Theory
- Mathematical Biology