Is there a tractable way to simulate (take a sample from) a Poisson process with intensity parameter that varies according to $\lambda(t)$ on an interval of time $[0,t]$? Assumptions about niceness of $\lambda$ are fine.
To be clear, I don't just want to get an integer $N_{t}$ for the counting process; I want to make a draw $a < X_1 < \dotsb < X_{N_t} < b$.