Compensated Jump process

I have been familiarizing myself with DifferentialEquations.jl

I was trying to find an example of an SDE simulation such that the SDE is a jump-diffusion such that the jumps are of the compensated (Poisson) form.

Is there an already built-in method I should be using or perhaps someone has an example I can look at?

Thank you.

I don’t think so. It’s worth an issue.

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Is your jump rate time homogeneous?

Yes they are.

Is a “Compensated Poisson Process” the same thing as a “Compound Poisson Process”?

No, they are not the same thing. A compensated Poisson process is a Poisson process which is made into a Martingale by subtracting the mean from the process.

If the jump process has rate \lambda, couldn’t you just add a -\lambda into the drift term for the same jump-diffusion but using an uncompensated Poisson process?

Edit: Assuming unit jumps…

yeah that is what I was thinking is the best solution at present. More variability would be nice but I am sure I can figure out how to get what I want of it.

what do you mean?

Jumps that aren’t necessarily unit jumps, that is jumps with variable size that can be dependent upon other factors.

yeah, the user would have to do that right now. It’s not hard, but it’s not automated.

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