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Brownian Motion and Potential Theory

  • Michael E. Taylor
Part of the Applied Mathematical Sciences book series (AMS, volume 116)

Abstract

Diffusion can be understood on several levels. The study of diffusion on a macroscopic level, of a substance such as heat, involves the notion of the flux of the quantity. If u(t, x) measures the intensity of the quantity that is diffusing, the flux J across the boundary of a region O in x space satisfies the identity
$$ \frac{\partial } {\partial }\int\limits_O {u(t,x)dV(x) = - \int\limits_{\partial O} {v \cdot JdS(x)} ,} $$
(0.1)
as long as the substance is being neither created nor destroyed.

Keywords

Brownian Motion Stochastic Differential Equation Dirichlet Boundary Condition Potential Theory Exit Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Michael E. Taylor
    • 1
  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

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