Stochastic Hybrid Processes with Hybrid Jumps
نویسنده
چکیده
Switching Diffusion processes can be represented as pathwise unique solutions of SDE’s in a hybrid state space that are driven by Brownian motion and Poisson random measure. This paper extends these SDE’s to switching jumpdiffusions, the jumps of which i) happen simultaneously with mode switching, and ii) depend on the mode after the switching. Jumps satisfying both i) and ii) are referred to as hybrid jumps. Because of ii) there is an anticipation effect in the SDE, which makes the hybrid jump extension challenging. Copyright ̧, 2003, IFAC.
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