Summary
The gamma process is determined by the form of conditional expectations and conditional variances. Also a new characterization of the gamma law is obtained and then applied to characterize the gamma process among the processes with independent increments.
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References
Bryc W (1985) Some remarks on random vectors with nice enough behaviour of conditional moments. Bull Polish Acad Sci, Math 33:677–684
Bryc W (1987) A characterization of the Poisson process by conditional moments. Stochastics 20:17–26
Bryc W, Plucińska A (1985) A characterization of infinite Gaussian sequences by conditional moments. Sankhya, Ser A 47:166–173
Feller W (1961) An introduction to probability theory and its applications, vol I. Wiley, New York
Laha RG, Lukacs E (1960) On a problem connected with quadratic regression. Biometrika 47:335–343
Moran PAP (1959) The theory of storage. Methuen, London
Kagan AM, Linnik YV, Rao CR (1973) Characterization problems in mathematical statistics. Wiley, New York
Plucińska A (1983) On a stochastic process determined by the conditional expectation and the conditional variance. Stochastics 10:115–129
Wesołowski J (1984) A characterization of the Gaussian process based on properties of conditional moments. Demonstratio Math 18:759–808
Wesołowski J (1988) A remark on a characterization of the Poisson process. Demonstratio Math 21:395–397
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Wesołowski, J. A characterization of the gamma process by conditional moments. Metrika 36, 299–309 (1989). https://doi.org/10.1007/BF02614103
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DOI: https://doi.org/10.1007/BF02614103