Point Processes On The Real Half-line
Historically the first point processes that were studied had the real half line R+ = in which the points represented events in time, such as calls to a telephone exchange.
Point processes on R+ are typically described by giving the sequence of their (random) inter-event times (T1, T2,...), from which the actual sequence (X1, X2,...) of event times can be obtained as
If the inter-event times are independent and identically distributed, the point process obtained is called a renewal process.
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