An algorithm for the estimation of parameters in models with stochastic differential equations

摘要

An algorithm for the estimation of parameters of stochastic differential equations (SDEs) is presented. It is based on a nonlinear weighted least-squares formulation, in which the objective function is evaluated based on mean values of the measured variables predicted through an Euler discretisation of the SDEs and their integration by Monte-Carlo simulation. The problem is solved using a Levenberg-Marquardt algorithm. The presence of simulation noise is handled by choosing a convergence criterion based on the noise level and by ensuring that the optimality criterion is met for a large simulation size and hence a low noise level. In order to increase the reliability of the algorithm and to decrease its computational cost, stochastic sensitivity equations are derived. Furthermore, the number of trajectories used in the Monte-Carlo simulations is changed adaptively throughout the execution of the algorithm. This leads to a significant decrease in computational requirements. These concepts are illustrated on a simple example and a more complex model of polymer rheology. In all cases, parameter estimates close to the true parameter values are identified. (c) 2007 Elsevier Ltd. All rights reserved.