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Brownian motion solves Laplace's Equation?

  1. Dec 29, 2012 #1
    There seems to be a curious connection between Brownian Motion, stochastic diffusion process, and EM.


    I was hoping to share and to have someone add some insight on on what it means that the Dirichlet boundary value problem can be solved using stochastic differential equations. It is interesting what this can mean in terms of wave propagtion.

    I do know that for an unbounded Brownian walk, the mean squared displacement MSD ~ t, whereas, for wave propagation and ballistic transport it is ~ t^2, but a Brownian walk with boundary conditions can have different diffusion.
    (On an even bigger leap of connection can this be somehow related to paths & path formulations of mechanics and EM)

    Thanks :redface:
  2. jcsd
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