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Optimal Estimation Problems for a Distributed parameter System
Existence theorems for the optimal estimations
3 other sections not shown
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assume AZ(o boundary conditions control problems corollary covariance operator d v(t dadB defined definition denotes distributed parameter system dW(t element error covariance function estimate U(t|t estimation error estimation problems evolution operator existence and uniqueness existence theorem fb(t filtering problem finite fixed-point smoothing following lemma following relation following theorem holds Furthermore G(t+v Gaussian process given Green's formula H-valued Hence Hilbert spaces inequality initial condition Ito's lemma lemma is completed linear distributed parameter linear stochastic obtained Omatu.S optimal control optimal estimators optimal filtering optimal sensor location optimal smoothing estimator partial differential equation proof random variable respect Riccati Riccati equation satisfies the following sensor location problem smoothing problem spatial domain step functions stochastic differential equation stochastic integral stochastic process theorem is completed tQ,tf Um(t unique solution UQ(x white Gaussian process Wiener process Wiener-Hopf equation yields yk(t
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Advances in the Statistical Sciences: Stochastic Hydrology: Volume IV ...
I.B. MacNeill,G. Umphrey
No preview available - 1986