State and parameter estimation from boundary-crossings

TitleState and parameter estimation from boundary-crossings
Publication TypeConference Paper
Year of Publication1998
AuthorsKrishnamurthy, V., and F. Le Gland
Conference NameDecision and Control, 1998. Proceedings of the 37th IEEE Conference on
Pagination3954 -3959 vol.4
Date Publisheddec.
Keywordsboundary-crossings, diffusion, diffusion process, drift coefficient, Feynman Kac type functionals, filtering theory, finite dimensional reconstructors, functional equations, maximum likelihood estimation, maximum likelihood parameter estimates, partial differential equations, probability, state estimation

We consider the problem of estimating the state, and identifying parameters of a diffusion process, when the only available information is the crossing times of a boundary. By using a partial differential equation approach related with the computation of boundary-crossing probabilities, we derive finite dimensional reconstructors (filters) for the state and Feynman Kac type functionals of the state. These are then used to compute maximum likelihood parameter estimates of the drift coefficient of the diffusion


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