Exact finite-dimensional filters for certain diffusions with nonlinear drift
- 1 June 1981
- journal article
- research article
- Published by Taylor & Francis in Stochastics
- Vol. 5 (1-2) , 65-92
- https://doi.org/10.1080/17442508108833174
Abstract
Let and be independent Wiener processes, and consider the task of estimating a diffusion solving the stochastic DE dx t =f(x t )dt+dw t on the basis of noisy observations defined bydy t =x t dt+db t . This problem is governed by the filtering equation for the unnormalized conditional density with A * the forwarded operator Theorem: if then the fundamental solution of the filtering equation can be written explicity in terms of a small number of statistics satisfying a matrixvector equation. The Lie algebraic interpretation of this result is studied and described. Extensions to many dimensions and applications to optimal stochastic control readily follow.Keywords
This publication has 3 references indexed in Scilit:
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- On the Gap Between Deterministic and Stochastic Ordinary Differential EquationsThe Annals of Probability, 1978
- On the optimal filtering of diffusion processesProbability Theory and Related Fields, 1969