Partial Characterizations of Completely Nondeterministic Stochastic Processes.
Abstract
A discrete weakly stationary Gaussian stochastic process x(t), is completely nondeterministic if no non-trivial set from the sigma-algebra generated by x(t):t > 0 lies in the sigma-algebra generated by x(t):t< or = 0. Levinson and McKean essentially showed that a necessary and sufficient condition for complete non-determinism is that the spectrum of the process is given by absolute value of H squared where h is an outer function in the Hardy space, H superscript + 2, of the unit circle in -C with the property that h/h bar uniquely determines the outer function h up to an arbitrary constant. In this paper we consider several characterizations of complete non-determinism in terms of the geometry of the unit ball of the Hardy space H superscript + 1 and in terms of Hankel operators, and pose an open problem. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1980
- Accession Number
- ADA097514
Entities
People
- Nicholas P. Jewell
- Peter Bloomfield
Organizations
- Princeton University