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A stochastic model of neural response

Published online by Cambridge University Press:  01 July 2016

John B. Walsh
John B. Walsh*
Affiliation:
The University of British Columbia
*
∗Postal address: Department of Mathematics, The University of British Columbia, #121–1984 Mathematics Road, University Campus, Vancouver, B.C., Canada V6T 1Y4.
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Abstract

We propose a model of a passive nerve cylinder undergoing random stimulus along its length. It is shown that this model is approximated by the solution of a stochastic partial differential equation. Numerous properties of the sample paths are derived, such as their modulus of continuity, quadratic and quartic variation, and it is shown that the solution exhibits the phenomenon of flicker noise. The first-passage problem is studied, and it is shown to be connected with a first-hitting time for an infinite-dimensional diffusion.

Keywords

NEURONSNERVE CYLINDERWHITE NOISESTOCHASTIC PARTIAL DIFFERENTIAL EQUATIONSBANACH-SPACE-VALUED BROWNIAN MOTIONORNSTEIN-UHLENBECK PROCESSINFINITE-DIMENSIONAL DIFFUSIONRANDOM FIELDS
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 2 , June 1981 , pp. 231 - 281
Copyright
Copyright © Applied Probability Trust 1981 

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