Henrik Madsen and Lasse Engbo Christiansen
Stochastic differential equations (SDEs) are used within many fields to model systems that are too complex to be described perfectly using ordinary differential equations and for systems with noise. One of the advantages relative to ordinary differential equations (ODEs) is that it is possible to separate measurement noise from system noise and hence gaining more insight into the origin of the noise. A large part of the work on SDEs at DTU Informatics is related to discretely observed continuous time stochastic state space models. Allowing for parameter estimation in a likelihood framework. And using likelihood ratio tests for model comparison.
The group currently have two software packages within these topics: CTSM (www.imm.dtu.dk/~ctsm) and PSM (www.imm.dtu.dk/projects/psm) where the latter is expected to replace CTSM as it is further developed.
Topics of interest include the use of additional random walk states in suggesting functional relationships, methods for model evaluation, and estimation of linear and non-linear mixed-effects models using stochastic differential equations.