OPTIMAL INTERPOLATION FOR LINEAR STOCHASTIC SYSTEMS.

Let y, satisfying dy equals Cx dt plus D dw, y(0) equals 0, represent the noisy observation of the Gauss-Markov process x generated by dx equals Ax dt plus B dw, x0 equals x//0, on the finite interval left bracket 0, T right bracket . The author solves the following interpolation problem: determine the best least-squares estimate of x(t),t an element of left bracket 0, T right bracket , given the increments of y on the intervals left bracket 0, T//1 right bracket and left bracket T//2, T right bracket , where 0 less than T//1 less than T//2 less than T, and the statistics of x//0. Several alternative expressions for the optimal interpolator are derived, some of which are phrased in terms of two Kalman-Bucy estimates. As a by-product, the interpolation problem for the missing increments of y is also solved.