Is there a name for a Poisson process which is piecewise homogeneous? I.e. time-homogeneous but with a parameter change each increment. Any references appreciated.
2026-04-15 12:48:07.1776257287
Piecewise homogeneous Poisson process
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The sequence of events corresponding to a sequence of independent, not necessarily identically distributed, interarrival times is called a generalized renewal sequence or a general renewal process. Thus, the random process you are interested in is the counting process of a general renewal process.
Inhomogeneous Poisson processes are different beasts, described by some, nonconstant but deterministic, intensity function $\lambda:t\mapsto\lambda(t)$.