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May 31, 2016 at 14:32 comment added whuber I don't know, because I invented it to answer this question. A little research suggests it is closely associated with the differential-difference equations derived for birth-death processes (but IMHO leads to a simpler analysis and an easier solution). It is also an example of a continuous-time Markov process. That should give you a set of effective search terms.
May 31, 2016 at 14:22 comment added Taylor Where can I learn more about this sliding window approach to examining stochastic processes?
May 30, 2016 at 17:48 comment added whuber It is true that the numbers of points in two overlapping intervals will not be independent. However, this lack of independence does not affect any analysis based on expectations.
May 30, 2016 at 17:46 comment added Taylor There's one parenthetical comment early on in the Poisson process section that says something like "independent of" which threw me off
May 30, 2016 at 17:41 comment added whuber You could do either, but I'm actually "sliding" it in the sense of letting it have any real value of $1$ or greater. This appears in the theoretical treatment (I integrate over $t$, rather than sum over it) and in the code (ecdf, the empirical cumulative distribution function, considers all real values of its arguments, not just integral values).
May 30, 2016 at 16:46 vote accept Taylor
May 30, 2016 at 16:46 comment added Taylor So you're not sliding $t$, you're incrementing it by $1$ every time, right? I'm going to accept the answer, but I might have some questions later on.
May 29, 2016 at 16:30 history answered whuber CC BY-SA 3.0