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On the innovation theorem

Author: T. F. Lin
Journal: Proc. Amer. Math. Soc. 65 (1977), 338-341
MSC: Primary 60J30; Secondary 60G35
MathSciNet review: 0461679
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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)\vert y(u), 0 \leqslant u \leqslant r)\;dr$, has the same probability law as $ w(t)$.

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Keywords: Process of independent increment, martingale, innovation process, observation process
Article copyright: © Copyright 1977 American Mathematical Society

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