The Kalman-Bucy Filter for Integrable L\'evy Processes With Infinite Second Moment
Abstract
We extend the Kalman-Bucy filter to the case where both the system and observation processes are driven by finite dimensional L\'evy processes, but whereas the process driving the system dynamics is square-integrable, that driving the observations is not; however it remains integrable. The key technique used is approximation by processes having bounded jumps.
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