Accession Number:

ADA159198

Title:

Linear Stochastic Differential Equations on the Dual of a Countably Hilbert Nuclear Space with Applications to Neurophysiology.

Descriptive Note:

Technical rept. Sep 84-Aug 85,

Corporate Author:

NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES

Personal Author(s):

Report Date:

1985-06-01

Pagination or Media Count:

218.0

Abstract:

Properties of the Ornstein-Uhlenbeck on the dual of a nuclear space are derived stationarity and existence of unique invariant measure is proved, Radon-Nikodym derivative exhibited and the OU process is investigated for flicker noise. Existence and uniqueness of solutions to linear stochastic differential equations on the dual of a nuclear space s established, and general conditions for the weak convergence on Skorohod space of solutions are given. Moreover, solutions are shown to be CADLAG semimartingales for appropriate initial conditions. The results are applicable to solving stochastic partial differential equations. Finally, the results are applied to giving a rigorous representation and solutions of models in neurophysiology as well as to deriving explicit results for the weak convergence of these solutions. Author

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE