Work

Some Large Deviation Asymptotics in Small Noise Filtering Problems

Year: 2022

Type: article

Abstract: 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 [R. Mortensen, J. Optim. Theory Appl., 2 (1968), pp. 386--394]. 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 solving the variational problem. Our main result gives a large deviation principle for Laplace functionals whose typical asymptotic behavior is described by Mortensen-type variational problems. Proofs rely on stochastic control representations for positive functionals of Brownian motions and Laplace asymptotics of the Kallianpur--Striebel formula.

Source: SIAM Journal on Control and Optimization

DOI: 10.1137/21m142616x

Authors: Anugu Sumith Reddy, Amarjit Budhiraja, Amit Apte

Institutions: University of North Carolina at Chapel Hill, Government of India, Department of Atomic Energy, International Centre for Theoretical Sciences, Tata Institute of Fundamental Research

Language: English

Topic: Target Tracking and Data Fusion in Sensor Networks

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Imperial College London, Tata Institute of Fundamental Research, Department of Atomic Energy, Government of India

Awards: G1772542340, Estimating Probabilities of Rare Events in Interacting Particle Systems, Optimization and Equilibria with Expectation Functions: Analysis, Inference and Sampling, G942205078