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'Mean Aversion' in Stochastic Differential Equations

  1. Sep 1, 2014 #1
    I had a brief question regarding SDEs. Typically, I've seen models like the Ornstein-Uhlenbeck process that generally revert back to the mean over time. However, I've been trying to find a stochastic differential equation/process that avoids the mean, such as a sharp increase followed by a sharp decrease. What examples are like this and/or how would one derive something like this?
     
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  3. Sep 1, 2014 #2

    Matterwave

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  4. Sep 1, 2014 #3
    Precisely. Is there any SDE/SP that represents a bimodal/trimodal/etc. distribution?
     
  5. Sep 1, 2014 #4

    Matterwave

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    Actually none come to my mind right now, although I'm sure there are.

    One example of perhaps an SDE that does not fall to a mean is geometric (or arithmetic even) Brownian motion, which is basically a superposition of Brownian motion on top of geometric growth, often used to model stocks.
     
  6. Sep 1, 2014 #5
    Could I just take geometric Brownian motion and instead of a Wiener process that is normally or lognormally distributed, use a Wiener process that is bimodally distributed?
     
  7. Sep 1, 2014 #6

    Matterwave

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    I am not familiar with any Wiener process than the regular Brownian motion...which is normally distributed...o.o
     
  8. Sep 3, 2014 #7
    Hahaha. Then just a random process that is bimodally distributed.
     
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