Towards a resolution of the reference pressure controversy in cerebrospinal fluid flow dynamics

Kalyan Raman*, P. Sundar

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Stochastic differential equations in which the drift is a quadratic function of the state variable and the infinitesimal standard deviation is proportional to the state variable are pervasive in electrical engineering, signal processing, the neurosciences, and the management sciences. Within this class, the homogeneous case in which the drift term contains no constant parameter is well-understood but the inhomogeneous case remains less researched. The basic issues of existence, positivity and explosion of solutions for the inhomogeneous case are addressed in this paper. It is shown that these results help settle an ambiguous issue arising in a fundamental neuroscience model and are of potential value in a class of signal processing models arising in electrical engineering.

Original languageEnglish (US)
Title of host publicationCerebrospinal Fluid
Subtitle of host publicationFunctions, Composition and Disorders
PublisherNova Science Publishers, Inc.
Pages107-121
Number of pages15
ISBN (Print)9781620810170
StatePublished - Aug 1 2012

Keywords

  • Gronwall inequality
  • Neuroscience
  • Quadratic drift.
  • Signal processing models
  • Stochastic differential equations
  • Strong solutions
  • The it̂o formula

ASJC Scopus subject areas

  • Medicine(all)
  • Neuroscience(all)

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