  This paper considers maximum likelihood inference for a functional marked
point process - the stochastic growth-interaction process - which is an
extension of the spatio-temporal growth-interaction process to the stochastic
mark setting. As a pilot study we here consider a particular version of this
extended process, which has a homogenous Poisson process as unmarked point
process and shifted independent Cox-Ingersoll-Ross processes as functional
marks. These marks have supports determined by the lifetimes generated by an
immigration-death process. By considering a (temporally) discrete sample scheme
for the marks and by considering the process' alternative evolutionary
representation as a multivariate diffusion (Markovian) with jumps, the
likelihood function is expressed as a product of the process' closed form
transition densities. Additionally, under the assumption that the mark
processes are started in their common stationary distribution, and under some
restrictions on the underlying parameters, consistency and asymptotic normality
of the maximum likelihood (ML) estimators are proved. The ML-estimators derived
from the stationarity assumption are then compared numerically to the
ML-estimators derived under non-stationarity, in order to investigate the
robustness of the stationarity assumption. To illustrate the model's use in
forestry, it is fitted to a data set of Scots pines.
