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I have a problem which includes geometric Brownian motion, with either normally distributed or power-law-distributed noise, and I'm asking for some explanations about this topic.

Specifically, the questions I would like to be answered are:

  1. What are the requirements on the noise distribution for the solution to be a log-normal.

  2. What happens if the noise is power-law?

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    $\begingroup$ Is this a physics question? $\endgroup$ – user1504 Jun 13 '13 at 14:13
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    $\begingroup$ @user1504 the two nearly related (the small scale spectrum depends on the stochastic forcing, sometimes cooled noise, indeed, when modelling stochastically driven Navier-Stokes turbulence for example) physics questions are in the second paragraph of this post. These are legitimate questions and I think asking for something to read along with the physics question does not invalidate this question. If I were not preparing for traveling to a conference, I could maybe even answer it... $\endgroup$ – Dilaton Jun 13 '13 at 15:54
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    $\begingroup$ @Dilaton I haven't voted to close, but all I see here is a math question. You bring up Navier-Stokes, but the OP might have been thinking about stock prices or the swimming habits of sharks. He doesn't say. $\endgroup$ – user1504 Jun 13 '13 at 15:59
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    $\begingroup$ If this relaxes the readers, this comes from a non-hyperbolic system. I asked here because I don't want neither finance literature nor mathematical theorems... I want physics' literature. $\endgroup$ – Jorge Leitao Jun 13 '13 at 16:03
  • $\begingroup$ Hi J. C. Leitão, book recommendation (title) questions are off-topic. If you (or someone else?) could edit the question to ask an actual conceptional (title) question I would be happy to consider re-opening the question. $\endgroup$ – Qmechanic Jun 15 '13 at 18:53

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