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
Let (X(t), t ≥ −1) and (Y (t), t ≥ 0) be stochastic processes satisfying dX(t) = aX(t)dt + bX(t − 1)dt + dW (t) and dY (t) = X(t)dt + dV (t), respectively. Here (W (t), t ≥ 0) and (V (t), t ≥ 0) are independent standard Wiener processes and ϑ = (a, b) is assumed to be an unknown parameter from some subset Θ of R 2. The aim here is to estimate the parameter ϑ based on continuous observation of (Y (t), t ≥ 0). Sequential estimation plans for ϑ with preassigned mean square accuracy ε are constructed using the so-called correlation method. The limit behaviour of the duration of the estimation procedure is studied if ε tends to zero.
We consider the parameter estimation problem for the scalar di usion type process described by t h e s t o c hastic equation Here we construct a sequential MLE with preassigned least square accuracy for the so-called stationary and the periodic cases of the solution X( ): The limit behaviour of the duration of the procedure with given accuracy is obtained.Keywords: stochastic di erential equations time delay maximum likelihood estimator sequential analysis least square accuracy.
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