Summary
Under very general conditions, we prove that the members of a so-called real polynomial chaos have absolutely continuous probability distributions.
References
Kusuoka, S.: Analytic functionals of Wiener process and absolute continuity. (Lect. Notes Math Vol. 923, pp. 1–46) Springer Verlag: Berlin Heidelberg New York 1982
Shigekawa, I.: Derivatives of Wiener functionals and absolute continuity of induced measures. J. Math. Kyoto Univ 20, 263–289 (1980)
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Partly supported by the Swedish Natural Science Research Council contract F-FU 1443-101, KTO:511443101-7
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Borell, C. Real polynomial chaos and absolute continuity. Probab. Th. Rel. Fields 77, 397–400 (1988). https://doi.org/10.1007/BF00319296
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DOI: https://doi.org/10.1007/BF00319296
Keywords
- Probability Distribution
- Stochastic Process
- General Condition
- Probability Theory
- Statistical Theory