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A Kalman filter for linear systems driven by time-space Brownian sheet (2407.06386v1)
Published 8 Jul 2024 in math.PR
Abstract: We study a linear filtering problem where the signal and observation processes are described as solutions of linear stochastic differential equations driven by time-space Brownian sheets. We derive a stochastic integral equation for the conditional value of the signal given the observation, which can be considered a time-space analogue of the classical Kalman filter. The result is illustrated with examples of the filtering problem involving noisy observations.