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If we have a Poisson point process with rate $\lambda$ and we keep each of its point with probability $p$, we obtain another Poisson point process with rate $\lambda p$. Does this result holds for a general Renewal point process? i.e.,

If in a renewal point process with rate $\lambda$, we keep each point with probability $p$ independently, do we obtain another renewal point process?

Susan_Math123
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    If each point is independently kept with probability $p$, then yes. Each new renewal time is independent of the previous ones. This seems similar to other questions you asked, what is the context here? – Michael Jun 13 '16 at 23:55

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