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Can someone please explain to me the difference between a Poisson Process and a Renewal Process ? is it just that the Holding times for Poisson processes are exponential and Holding times for Renewal Processes are any kind of probability distribution (as the wiki page seems to imply)

If this is the case I don't understand why on the wiki page when reffering to the "Proof of the renewal equation" they invoke the Markov property - which I thought only held for memoryless (i.e. exponential ) distributions

Thanks