## Has anyone found a way to determine the invariant measure of a one-dimensional jump-diffusion?

I am working with a jump-diffusion on the unit interval, with absorbing endpoints, and I was hoping someone has found a way to determine the invariant measure, similar to that of an Ito process.

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The general procedure is the following. Take the generator $L$ of the semigroup associated to your process. Then find its dual $L^*$. The latter governs the evolution of 1-dim distributions (via forward Kolmogorov equation), and an invariant density $p$ satisfies $L^*p=0$, should be positive and integrate to 1.

I suspect all this can be found in the Ethier&Kurtz book on Markov processes, but I do not have it at hand right now.

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Henry Tuckwell's 1976 paper, "On the First-Exit Time Problem for Temporally Homogeneous Markov Processes", gives an ODDE to solve to determine the invariant (ergodic) measure.

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