Regularity Properties of a Stochastic Partial Differential Equation

  • John B. Walsh
Part of the Progress in Probability and Statistics book series (PRPR, volume 7)


This article is a sequel to [8] which studied the electrical potential in a randomly-stimulated neuron of the brain or spinal chord by means of the stochastic partial differential equation
$$ \frac{{\partial V}}{{\partial t}} = \frac{{{\partial ^{2}}V}}{{\partial {x^{2}}}} - V + {\mathop{{\rm{W}}}\limits^{\bullet } _{{xt'}}} $$
where W̊ is a space-time white noise. The neuron was represented by a line segment, and V(x,t) was the electrical potential at x at time t.


Lebesgue Measure Stochastic Partial Differential Equation Weak Derivative Spinal Chord Strong Martingale 
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Copyright information

© Birkhäuser Boston, Inc. 1984

Authors and Affiliations

  • John B. Walsh
    • 1
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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