SIEVE-BASED MAXIMUM LIKELIHOOD ESTIMATOR FOR ALMOST
PERIODIC STOCHASTIC PROCESS MODELS
Abstract: Assume that the point process 
is observed with stochastic intensity
of the form 
where 
is an unknown almost periodic nonnegative
function and 
is an observable nonnegative stochastic process. It is shown that the
sieve-based maximum likelihood estimator of 
is consistent in the appropriate metric of
the space of uniformly almost periodic (UAP) functions. The same technique establishes the
consistency of the sieve-based maximum likelihood estimator of a UAP drift function in a
stochastic differential equation.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -
