On the innovation theorem
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- by T. F. Lin PDF
- Proc. Amer. Math. Soc. 65 (1977), 338-341 Request permission
Abstract:
Let $z(t),0 \leqslant t \leqslant T$, be the signal process and $y(t) = \smallint _0^tz(r)\;dr + w(t)$ be the observation process where $w(t)$ is a process of independent increments. It is shown that, under certain conditions, the innovation process $v(t) = y(t) - \smallint _0^tE(z(r)|y(u), 0 \leqslant u \leqslant r)\;dr$, has the same probability law as $w(t)$.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 338-341
- MSC: Primary 60J30; Secondary 60G35
- DOI: https://doi.org/10.1090/S0002-9939-1977-0461679-9
- MathSciNet review: 0461679