scholarly journals ROBUST CONTINUOUS-TIME SMOOTHERS FOR BENEŠ AND PIECEWISE LINEAR STOCHASTIC SYSTEMS

2002 ◽  
Vol 35 (1) ◽  
pp. 67-72
Author(s):  
Vikram Krishnamurthy ◽  
Robert Elliott
Keyword(s):  
Continuous Time ◽  
Stochastic Systems ◽  
Piecewise Linear ◽  
Linear Stochastic Systems

scholarly journals Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Xiu Kan ◽  
Huisheng Shu ◽  
Yan Che
Keyword(s):  
Parameter Estimation ◽  
Continuous Time ◽  
Unknown Parameter ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Asymptotic Convergence ◽  
Linear Filtering ◽  
Linear Stochastic Systems ◽  
Asymptotic Parameter ◽  
Consistent Property

The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameterθ:dXt=(θα(t)+β(t)Xt)dt+σ(t)dWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameterθbased on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.

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