Accession Number:

ADA224431

Title:

Propagation of Chaos and the McKean-Vlasov Equation in Duals of Nuclear Spaces

Descriptive Note:

Corporate Author:

NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES

Report Date:

1990-05-01

Pagination or Media Count:

49.0

Abstract:

The paper is concerned with propagation of chaos problems for systems with an infinite number of degrees of freedom such as strings or spatially extended neurons. The investigation of the asymptotic behavior of the voltage membrane potentials of large assemblages of interacting neurons leads to precisely such problems and provided the immediate motivation for the work. Another example to which the approach of the present paper could be applied is the Ginsburg-Landau model in hydrodynamics. Basic properties of duals of nuclear spaced denoted throughout by Psi, the strong dual of a countably Hilbertian nuclear space Psi are briefly discussed and the results of Kallianpur et al. on the existence and uniqueness of the solution to the martingale problem posed by a Psi-valued stochastic differential equation SDE is extended to a system of such equations. The principal results in which the infinite dimensionality of our problem call for special arguments are derived. JHD

Subject Categories:

  • Anatomy and Physiology
  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE