On Sequential Estimators for Affine Stochastic Delay Differential Equations

Küchler, Uwe; Vasiliev, Vyacheslav A.

doi:10.1007/978-3-540-46551-5_22

Cited by 4 publications

(6 citation statements)

References 6 publications

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“…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).…”

Section: Resultsmentioning

confidence: 99%

“…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.…”

Section: Construction Of Sequential Estimation Plansmentioning

confidence: 99%

“…of the estimator λ t defined in (11), it is easy to obtain with P ϑ -probability one the following limit relations:…”

Section: Proof Of Proposition 33mentioning

confidence: 99%

“…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).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Küchler¹,

Vyacheslav²

2012

Stochastic Modeling and Control

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Section: Resultsmentioning

confidence: 99%

“…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.…”

Section: Construction Of Sequential Estimation Plansmentioning

confidence: 99%

“…of the estimator λ t defined in (11), it is easy to obtain with P ϑ -probability one the following limit relations:…”

Section: Proof Of Proposition 33mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Küchler¹,

Vyacheslav²

2012

Stochastic Modeling and Control

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“…For time-delayed systems of the type (1) a sequential estimation procedure for some special chosen sets Θ of vector parameter ϑ = (ϑ 0 , ϑ 1 ) has been constructed by Küchler and Vasiliev (2001, 2003, 2006.…”

Section: Moreover Assume Thatmentioning

confidence: 99%

On sequential parameter estimation of a linear regression process

Küchler

Vasiliev

2008

IFAC Proceedings Volumes

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On guaranteed parameter estimation of a multiparameter linear regression process

Küchler

Vasiliev

2010

Automatica

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On guaranteed parameter estimation of a multiparameter linear regression process 1;2 we u uhler yheslv eF siliev snstitute of wthemtis heprtment of epplied wthemtis rumoldt niversity ferlin nd gyernetis nter den vinden TD hEIHHWW omsk tte niversity ferlinD qermny venin QTD TQRHSH omskD ussi Abstract his pper presents sequentil estimtion proedure for the unknown prmeters of ontinuousEtime stohsti liner regression proessF es exmples the sequenE til estimtion prolem of two dynmi prmeters in stohsti liner systems with memory nd in utoregressive proesses is solvedF he estimtion proedure is sed on the lest squres method with weights nd yields estimtors with gurnteed E ury in the sense of the L q norm for xed q ! PF he proposed proedure works in the mentioned exmples for ll possile vlues of unknown dynmi prmeters on the plne R P for the utoregressive proesses nd on the plne R P with the exeption of some lines for the liner stohsti dely equtionsF he symptoti ehvior of the durtion of oservtions is determinedF he generl estimtion proedure is designed for twoE or moreEprmetri modelsF st is shownD tht the proposed proedure n e pplied to the sequentil prmeter estimtion prolem of ne stohsti dely dierentil equtions nd utoregresE sive proesses of n ritrry orderF

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On Sequential Estimators for Affine Stochastic Delay Differential Equations

Cited by 4 publications

References 6 publications

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

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

On sequential parameter estimation of a linear regression process

On guaranteed parameter estimation of a multiparameter linear regression process

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