# Some Large Deviations Asymptotics in Small Noise Filtering Problems

@inproceedings{Reddy2021SomeLD, title={Some Large Deviations Asymptotics in Small Noise Filtering Problems}, author={Anugu Sumith Reddy and Amarjit Budhiraja and Amit Apte}, year={2021} }

We consider nonlinear filters for diffusion processes when the observation and signal noises are small and of the same order. As the noise intensities approach zero, the nonlinear filter can be approximated by a certain variational problem that is closely related to Mortensen’s optimization problem(1968). This approximation result can be made precise through a certain Laplace asymptotic formula. In this work we study probabilities of deviations of true filtering estimates from that obtained by… Expand

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Change of measures has been an effective method in stochastic control and analysis; in continuous-time control this follows Girsanov’s theorem applied to both fully observed and partially observed… Expand

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