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

Abstract

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.