Estimation of parameters of linear homogeneous stochastic differential equations
type: Item
instance of: scholarly article
title: Estimation of parameters of linear homogeneous stochastic differential equations
zbMATH Open document ID: 0933.62099
DOI: 10.1016/S0304-4149(97)00083-5
published in: Stochastic Processes and their Applications
publication date: 2000-03-01T00:00:00Z
review text: The authors investigate the problem of parametric estimation for multidimensional linear homogeneous differential equations of the form \(dX_t = AX_tdt + \sigma (X_t)dW_t.\) The estimation of the unknown parameter matrix \(A\) using the observations \(X^{(T)}\) of the process \(X_t\), \(0\leq t \leq T\), is considered. They prove the local asymptotic normality property, find the maximum likelihood estimator and prove its asymptotic efficiency for bounded loss functions, when the observation time tends to infinity.
Mathematics Subject Classification ID: 62M99
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62M15
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 1409158
zbMATH Keywords: linear stochastic differential equations
zbMATH Keywords: local asymptotic normality
zbMATH Keywords: maximum likelihood estimators
zbMATH Keywords: asymptotic efficiency
author: Andrius Jankunas
author: R. Z. Khas'minskiĭ
reviewed by: Gejza Dohnal
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1409158