Estimating stochastic dynamical systems driven by a continuous-time jump Markov process
The authors consider the stochastic dynamical system \[ Z'(t)=f(Z(t),X(t)). \] Here \(X\) is a time-continuous Markov process with finite state space. First, it is assumed that \(X\) is observed on time intervals \([0,T_k]\) , \(k=1,\dots,n\), for \(n\) i.i.d. realisations. Consistency and asymptotic normality of the maximum-likelihood estimator are derived. This is applied to observations of the dynamical system \(Z\) in the case where we can write \(X(t)=h(Z(t),Z'(t))\) with some known function \(h\). A numerical study of the corresponding plug-in estimator, especially for a fatigue crack growth model, is performed.
scientific article; zbMATH DE number 5119597
scientific article