0

Let $a,\lambda,\delta > 0$ . Compute the expected number of arrivals in a Poisson process with intensity function $\alpha(t)=ae^{-\lambda t}$, which are not followed by another arrival with time interval of length $\delta$.

Suppose the number of such arrivals is $N(a)$. Then $E(N(a))=1+E_T(E(N(ae^{-\lambda (T+\delta)})))$ where $T$ is the time of first such arrival. I cant understand how can I find out the next expectation in the recursion.

Subhasish Basak
  • 638
  • I don't understand what you mean by "expected number of arrivals which are not followed by another arrival with time interval of length $\delta$", can you clarify? – Math1000 Sep 01 '15 at 21:12
  • I mean I want to count only those arrivals which do not have another arrival within next $\delta$ time. Say, I got an arrival at time 5 then I will count it if there is no other arrival in the interval $(5,5+\delta]$. – Subhasish Basak Sep 01 '15 at 21:24

0 Answers0