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I want to do some MC simulation of an Ornstein Uhlenbeck process with NIG errors. Is the analytical solution of the SDE with gaussian noise equal to the SDE with gaussian errors and NIG errrors.Basically, under the simulation; is it just to replace a vector with gaussian noise with a random vector with NIG errors? Or do I have to do some modification to the following equation: x_t=x_0 e^{-\theta t} +\mu (1-e^{-\theta t})+ {\sigma\over\sqrt{2\theta}}e^{-\theta t} {e^{2\theta t}-1} W_t. Is it just to change W_t from gaussian to NIG-distributed?

I interpret your question as: how do I simulate the Levy-driven OU process:(*) [$]dX_t = (a - b X_t) \, dt + dL_t [$],where [$]L_t[$] is the NIG Levy process?If that's it, googling shows there is literature on how to simulate NIG Levy processes. Presumably modifying those simulations to account for the OU drift would be easy. Also Cont & Tankov in their book discuss simulating general Levy processes. Re your unreadable eqn: there is indeed an sde solution to (*) analogous to OU sde soln, but whether or not that soln is helpful for a simulation scheme, I don't know.

Hi AlanThanks for the reply.What I am trying to ask is: I have a solution for a OU-process with Gaussian errors. Is it just to replace drawing errors from a gaussian distribution, and replace it with NIG-errors in terms of MC for a NIGOU-model?

I'm not sure -- that's why I didn't give a direct answer, but suggested *how* to find the answer. Here's another link in the same spirit: Mathematica demo with code and references

not very familiar with levy process. But the analytic solution to the gaussian one is derived with aid of ito's lemma. As I remember, Ito's lemma is different when applied to jump processes. You need to check with that. Please correct me if I am wrong

Do you have any other links, Alan?