I have a question regarding the nonhomogenous Poisson process. From the definition I understand that $\lambda(s)$, the intensity of the process, is a deterministic function and the increments of the process $N_T-N_t \sim Pois\int_t^T \lambda(s)ds$. Does this hold true even for a generalisation where the intensity is assumed to be nondeterministic e.g. some jump diffusion process?
2026-03-25 17:35:29.1774460129
Nonhomogenous Poisson Process
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