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Interpretation of the distribution of brownian motion

  1. Nov 30, 2011 #1
    Hi all,

    I feel like there's a missing link in my understanding of brownian motion. I'm comfortable with the "method of rice" where the signal is written as a fourier series, and with fokker-planck equations and diffusion. I'm somewhat comfortable with an introductory theory of stochastic processes.

    What bothers me is that I can't explain to myself what the distribution of sample paths means. For example, a statistician might want to do inference on an unknown scalar field. They place a gaussian process prior on the field, and from that can get a pretty good fit. I think of a GP as a distribution over functions.
    So brownian motion is a GP, with some added conditions. But if it's a GP, I don't understand how W(t), dW(t), or \int W(t) create a distribution over functions. I can see how there's some probability that the sample path will be in a particular interval (y,y+dy), but that's not quite the same to me.

    Help me out?
    Last edited: Nov 30, 2011
  2. jcsd
  3. Dec 4, 2011 #2


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