Title of article :
RANDOM DELAY DIFFERENTIAL EQUATIONS and INVERSE PROBLEMS FOR AGGREGATE DATA PROBLEMS
Author/Authors :
Banks, H.T. Center for Research in Scientific Computation - Department of Mathematics - North Carolina State University Raleigh , Thompson, W.C. Center for Research in Scientific Computation - Department of Mathematics - North Carolina State University Raleigh
Abstract :
We consider nonparametric estimation of probability measures for parameters in
delay differential equation (DDE) problems where only aggregate (population level) data are
available. We summarize an existing computational method for the estimation problem which
has been developed over the past several decades [11, 17, 21, 26, 28]. Theoretical results are
presented which establish the existence and consistency of very general (ordinary, generalized
and other) least squares estimates and estimators for the measure estimation problem with
specific application to random DDEs.
Keywords :
Inverse problems , random delay differential equations , aggregate data , approx- imation and consistency of estimators
Journal title :
Eurasian Journal of Mathematical and Computer Applications
