Stochastic Differential Equations for Neuronal Behavior.

Abstract

This article extends the recent work of Kallianpur and Wolpert modeling the behavior of neurons by means of stochastic partial differential equations on the dual of a nuclear space. The extensions will cover nuclear spaces of a more general structure and will apply to models described in terms of more general differential operators. A second objective of this article is to present a theoretical framework which will include the model recently proposed and heuristically investigated by Wan and Tuckwell. The authors illustrate their approach and its application by giving a rigorous treatment of the Wan and Tuckwell model. But first they briefly describe the neurophysiological context. Additional keywords: Voltage potential; Weak convergence; Mathematical models; Theorems. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1985
Accession Number
ADA159099

Entities

People

  • G. Kallianpur
  • S. K. Christensen

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Cellular Structures
  • Convergence
  • Differential Equations
  • Equations
  • Hilbert Space
  • Mathematical Models
  • Models
  • North Carolina
  • Partial Differential Equations
  • Probability
  • Random Variables
  • Statistics
  • Stochastic Processes
  • Time Intervals
  • Topology
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space