
Patterns of Several Types of Points 631
Note that, in making the definition (14.82 ), we have effectively assigned eq ual weight to all
possible types m. This is mathematically convenient because (14.82) will reduce to (14.81) when
λ
(u,m) =
λ
m
does not depend on location u. However it requires care when interpreting the results
of a fitted model.
14.12.3 Stationarity
A multitype po int process is defined to be stationary if its distribution is unaffected by shifting the
locations x
i
.
Definition 14.1. A multitype point process in R
2
with marks in M is stationary if its distribution is
invariant under translations of R
2
, that is, under transformations (u, m