Simple Point Process

A simple point process (or SPP) is an almost surely increasing sequence of strictly positive, possibly infinite random variables which are strictly increasing as long as they are finite and whose almost sure limit is . Symbolically, then, an SPP is a sequence of -valued random variables defined on a probability space such that

1. ,

2. ,

3. .

Here, and for each , can be interpreted as either the time point at which the th recording of an event takes place or as an indication that fewer than events occurred altogether if or if , respectively (Jacobsen 2006).