An interval stationary point process is a point process 
on 
such that for every 
and for all integers 
,
the joint distribution of
 |
does not depend on 
, 
. Here 
is the nonnegative random variable giving the time between consecutive
points 
and 
of 
.
As pointed out in a variety of literature (e.g., Daley and Vere-Jones 2003, pp. 45-46), the notion of an interval stationary point process is intimately connected to (though fundamentally different from) the idea of a stationary point process in the Borel set sense of the term. Worth noting, too, is the difference between interval stationarity and other notions such as simple/crude stationarity.
Though it has been done, it is more difficult to extend to 
the notion of interval stationarity; doing so requires a
significant amount of additional machinery and reflects, overall, the significantly-increased
structural complexity of higher-dimensional Euclidean
spaces (Daley and Vere-Jones 2007).
