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I am looking into generalizing the Ornstein-Uhlenbeck process to non-Gaussian noise sources. In the code, I discretized the OU process (Euler-Maryuama discretization) and converted it into an AR(1) model, similar to the answer here, where we end up with

$x_{k+1} = \theta(\mu - x_k)\Delta t + \sigma \varepsilon_k\sqrt{\Delta t}$

Since $\varepsilon_k$ is normally distributed, can I not just replace this with another distribution and get a non-Gaussian OU process? It surely is not that simple?

MilTom
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  • You will get a non-Gaussian process. What properties do you want the process to have? – user619894 Oct 22 '20 at 09:56
  • @user619894 I am looking into distributions with fatter tails for which the Gaussian noise assumption does not work as well. – MilTom Oct 22 '20 at 09:57

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