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Nonexistence of finite-dimensional filters for conditional statistics of the cubic sensor problem |
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| Authors: | M Hazewinkel S I Marcus H J Sussmann |
| Affiliation: | a Mathematical Centre, P.O. Box 4079, 1009 AB, Amsterdam, The Netherlands b Dept. Math., Erasmus Univ. Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands Dept. Electrical Engineering, University of Texas, Austin, TX 78712, USA Dept. Mathematics, Rutgers University, New Brunswick, NJ 08903, USA |
| Abstract: | Consider the cubic sensor dx = dw, dy = x3dt + dv where w, v are two independent Brownian motions. Given a function φ(x) of the state x let φt(x) denote the conditional expectation given the observations ys, 0  s t. This paper consists of a rather detailed discussion and outline of proof of the theorem that for nonconstant φ there cannot exist a recursive finite-dimensional filter for φ driven by the observations. |
| Keywords: | Cubic sensor Recursive filter Robust filtering Weyl Lie algebra |
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