On sequential parameter estimation of a linear regression process

On Guaranteed Parameter Estimation of Stochastic Delay Differential Equations by Noisy Observations

“…The obtained estimation procedure can be easily generalized, similar to [9,11,13,16], to estimate the unknown parameters with preassigned accuracy in the sense of the L q -norm (q ≥ 2). The estimators with such properties may be used in various adaptive procedures (control, prediction, filtration).…”

“…Then we shall define, similar to [11,13,14,16], the final sequential estimation plan, which works in Θ as a sequential plan with the smallest duration of observations.…”

“…The set Θ is defined to be the intersection of the set Θ with an arbitrary but fixed ball B 0,R ⊂R 2 . Sequential estimation problem has been solved for sets Θ of a different structure in [7]- [9], [11,13,14,16] by observations of the process (1) and in [10,12,15] -by noisy observations (2).…”

“…The general sequential estimation problem for all ϑ =( a, b) ′ from R 2 except of two lines was solved in [13,14,16] for the equation (1) based on the observations of X(·).…”

“…In this chapter the sequential estimation method developed in [10,12] for the system (1), (2) is extended to the case, considered by [13,14,16] for the equation (1) (as already mentioned, for all ϑ from R 2 except of two lines for the observations without noises).…”