Abstract
A discrete-time model for filtering with small observation noise is considered. A piecewise linear observation function is considered with two intervals of monotonicity. A sequential quadratic variation test is found to detect intervals of linearity of the observation function. Diffusion approximations to certain discrete processes are made to estimate the mean times for reaching a decision and the error probabilities.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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