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

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)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1985
Accession Number
ADA159198

Entities

People

  • S. K. Christensen

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Cellular Structures
  • Chemical Reactions
  • Construction
  • Differential Equations
  • Equations
  • Fokker Planck Equations
  • Functional Analysis
  • Gaussian Processes
  • Hilbert Space
  • Information Science
  • North Carolina
  • Partial Differential Equations
  • Probability
  • Random Variables
  • Statistics
  • Stochastic Processes
  • Topology

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space