Accession Number : AD0729649

Title :   The Equivalence or Singularity of Stochastic Processes and of the Measures they Induce on L sub 2.

Descriptive Note : Technical rept.,

Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Cambanis,Stamatis

Report Date : JUL 1971

Pagination or Media Count : 26

Abstract : It is shown that the proposition: 'Two stochastic processes are equivalent or singular if and only if the measures they induce on a appropriate (L sub 2) space are equivalent or singular respectively,' is not true in general, and sufficient conditions are given for its validity. For a wide class of square integrable martingales it is shown that this proposition is valid and a number of results are obtained which generalize known results for the Wiener process. (Author)

Descriptors :   (*STOCHASTIC PROCESSES, *MEASURE THEORY), HILBERT SPACE, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE