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Sample functions of
Pólya processes
Takayuki Kawada |
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Vol. 97 (1981), No. 1, 125–135
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Abstract |
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For a nonnegative measurable function f satisfying
define
Berman proved, extending so-called “Polya characteristic function”, that the r is the characteristic function of an absolutely continuous distribution. The positive-definiteness of the r corresponds to a stationary Gaussian process, which is called Polya-Covariance process or simply Polya process. In this paper, some analytic properties of its sample functions are studied: (1) continuity, (2) differentiability, (3) quadratic variation, and (4) upper and lower class. |
Mathematical Subject Classification 2000
Primary: 60G15
Secondary: 60G17
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Milestones
Received: 29 July 1980
Published: 1 November 1981
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Authors |
| Takayuki Kawada | |
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