Point Process Methods 147
have n((X + v) ∩B) = n(X ∩(B −v)) so that n(X ∩(B −v )) has the same distribution as n(X ∩B),
implying that En(X ∩B −v) = En(X ∩B). It ca n be shown that this implies En(X ∩B) =
λ
|B| for
some constant
λ
, so the point process has homogeneous intensity.
The assumption of stationarity is crucial for many of the classical tools of sp a tial statistics, such
as Ripley’s K-function (Chapter 7). If the point process is not stationary, the K-function is n ot even
a well-defined concept.
A point process is called stationary and isotropic if its statistical properties are unaffected by
shifting or rotating the point process. If we view such a process through a windowW, the observable
statistical properties do not depend on the location ...