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I wonder if anyone has come across this problem before and could point me to a relevant ref or tell me what terms I might search for:

I am interested in a continuous time process in which two alternating events (call them A and B) occur. Each event has an exponentially distributed duration, with different rate constants. They occur consecutively and exclusively: A immediately follows B and vice-versa, with no overlapping or gaps.

Our experiment always starts with A. After an exponentially distributed waiting time, B occurs. After a second time wait, exponentially distributed but with different rate constant, A occurs again, etc.

I am seeking the expected number of events (or pairs of events) that occur in a given time interval.

I have attempted this myself, but my approach became complicated quite rapidly so I thought I would check here first to see if anyone had come across this before.

Thanks, and apologies for the lengthy description.

Gabriel

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# Problem related to the compound Poisson process (?)

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