Estimating stochastic dynamical systems driven by a continuous-time jump Markov process
type: Item
instance of: scholarly article
title: Estimating stochastic dynamical systems driven by a continuous-time jump Markov process
zbMATH Open document ID: 1118.62087
author: Julien Chiquet
author: N. Limnios
published in: Methodology and Computing in Applied Probability
publication date: 2007-01-29T00:00:00Z
full work available at URL: Chiquet-Limnios2006 Article EstimatingStochasticDynamicalS.pdf
review text: 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.
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 62N05
zbMATH DE Number: 5119597
zbMATH Keywords: Markov process
zbMATH Keywords: maximum-likelihood estimator
zbMATH Keywords: fatigue crack growth
reviewed by: Markus Reiß
MaRDI profile type: Publication
OpenAlex ID: W2068896871
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DOI: 10.1007/S11009-006-0423-Z
description: scientific article; zbMATH DE number 5119597