Stochastic delay differential equations sequential analysis noisy observations mean square accuracy On parameter estimation of stochastic delay differential equations with guaranteed accuracy by noisy observations Uwe Küchler Küchler Uwe Vjatscheslav A. Vasil’iev Vasil’iev Vjatscheslav A. Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 27 pages

On parameter estimation of stochastic delay differential equations with guaranteed accuracy by noisy observations

Uwe Küchler , Vjatscheslav A. Vasil’iev

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 27 pages

MSC 2000

34K50 Stochastic delay equations
60H10 Stochastic ordinary differential equations
62L10 Sequential analysis
62L12 Sequential estimation

Abstract
Let $(X(t), t\geq −1)$ and $(Y (t), t \geq 0)$ 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 $(W(t), t \geq 0)$ and $(V (t), t \geq 0)$ are independent standard Wiener processes and $\theta = (a, b)'$ is assumed to be an unknown parameter from some subset $\Theta$ of $R^2$. The aim here is to estimate the parameter $\theta$ based on continuous observation of $(Y (t), t \geq 0)$. Sequential estimation plans for $\theta$ with preassigned mean square accuracy $\epsilon$ are constructed using the so-called correlation method. The limit behaviour of the duration of the estimation procedure is studied if $\epsilon$ tends to zero.


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