1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

2-D Brownian motion with correlated noise

  1. Oct 18, 2012 #1
    dx/dt = η(t)
    dy/dt = ζ(t)

    <η(t)η(t')> = 2Dδ(t-t')
    <ζ(t)ζ(t')> = 2Dδ(t-t')

    If <η(t)ζ(t')> = 0, we have the standard 2-D diffusion equation and the analytical solution is known.

    If <η(t)ζ(t')> = 2Dδ(t-t'), or η(t) = ζ(t), we can transform it into a 1-D problem and the analytical solution is also known.

    What if <η(t)ζ(t')> = 2Dcδ(t-t') where 0<c<1 which is correlation of the two noises? We can still write down a 2-D diffusion equation, but is the analytical solution known?
    Last edited: Oct 18, 2012
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted