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Suppose that I know all intensity functions lambda(t) during given period [0,t], how can I compute the mean function m(t) for non-homogeneous Poisson process?

Basically, m(t) in the integral of lambda(t) from 0 to t. Through simulation, I can actually compute all lambda(t). Is there an efficient algorithm to compute m(t)?

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  • $\begingroup$ "Suppose that I know all intensity functions lambda(t)"+", m(t) in the integral of lambda(t) from 0 to t"+"Is there an efficient algorithm to compute m(t)?"="Is there an efficient way to compute a definite integral over an interval?". Am I misunderstanding something? $\endgroup$
    – fedja
    Commented Dec 20, 2014 at 4:12
  • $\begingroup$ Since lambda(t) change frequently during [0,t],like hundreds of times, so lambda(t) is actually an addition of many definite integral of lambda (t) over an internal included in [0,t]. $\endgroup$
    – ycenycute
    Commented Dec 20, 2014 at 9:02
  • $\begingroup$ So, what exactly is the setup? Are you given some crazy oscillatory formula for $\lambda(t)$ (then what is it?) or something else? I still have no idea what the conditions of your problem are. $\endgroup$
    – fedja
    Commented Dec 20, 2014 at 10:26

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