Nonlinear filtering and large deviations
- 1 December 1987
- proceedings article
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1588-1589
- https://doi.org/10.1109/cdc.1987.272708
Abstract
We consider the nonlinear filtering problem dx = f(x)dt + √∈dw, dy = h(x)dt + √∈dv, and obtain lim→∈0 ∈log q∈(x, t) = -W(x,t) for unnormalised conditional densities q∈ (x,t) using PDE methods. Here, W(x,t) is the value function for a deterministic optimal control problem arising in Mortensen's deterministic estimation, and is the unique viscosity solution of a Hamilton-Jacobi-Bellman equation.Keywords
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