Accession Number : AD0746022

Title :   On Some Continuity and Differentiability Properties of Paths of Gaussian Processes,

Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Cambanis,Stamatis

Report Date : JUN 1972

Pagination or Media Count : 26

Abstract : The paper considers some path properties of real separable Gaussian processes xi with parameter set an arbitrary interval. The following results are established, among others. At every fixed point the paths of xi are continuous, or differentiable with probability zero or one. If xi is measurable, then with probability one its paths have essentially the same points of continuity and differentiability. If xi is measurable and not mean square continuous or differentiable at every point, then with probability one its paths are almost nowhere continuous or differentiable respectively. If xi is mean square continuous and stationary, then its paths are differentiable with probability one if and only if xi is mean square differentiable. If xi is harmonizable, then its paths are absolutely continuous if and only if xi is mean square differentiable. (Author)

Descriptors :   (*STATISTICAL PROCESSES, THEOREMS), MEASURE THEORY, PROBABILITY, RANDOM VARIABLES, SET THEORY

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE