Mapping theorem (point process)
The mapping theorem is a theorem in the theory of point processes, a sub-discipline of probability theory. It describes how a Poisson point process is altered under measurable transformations. This allows to construct more complex Poisson point processes out of homogeneous Poisson point processes and can for example be used to simulate these more complex Poisson point processes in a similar manner than inverse transform sampling.Statement
Let be locally compact and polish and let
be a measurable function. Let be a Radon measure on and assume that the pushforward measure
of under the function is a Radon measure on.
Then the following holds: If is a Poisson point process on with intensity measure, then is a Poisson point process on with intensity measure.
