A Bayes Formula for Non-linear Filtering with Gaussian and Cox Noise
نویسنده
چکیده
A Bayes type formula is derived for the non-linear filter where the observation contains both general Gaussian noise as well as Cox noise whose jump intensity depends on the signal. This formula extends the well know Kallianpur-Striebel formula in the classical non-linear filter setting. We also discuss Zakai type equations for both the unnormalized conditional distribution as well as unnormalized conditional density in case the signal is a Markovian jump diffusion.
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