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

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 v = (a, b)' is assumed to be an unknown parameter from some subset Theta of R-2. The aim here is to estimate the parameter V based on continuous observation of (Y(t), t >= 0). Sequential estimation plans for V with preassigned mean square accuracy E are constructed using the so-called correlation method. The limit behaviour of the duration of the estimation procedure is studied if C tends to zero. (c) 2007 Elsevier B.V. All rights reserved.