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Estimation of Markov processes

✍ Scribed by Omar Hijab

Publisher
Elsevier Science
Year
1981
Tongue
English
Weight
386 KB
Volume
1
Category
Article
ISSN
0167-6911

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✦ Synopsis

Let I + x(r) denote a Mark& process evolving on some state-space X and consider observations given by .Y( r) = h( x( I)), where h is a real-valued function on X. If $I is another real-valued function on X, the best estimate (in the mean square sense) of $(x( 1)) given y(r), OGTC t, is the conditional expectation E($~(.x(t))ly(r), O< 7~ 1). In this paper we derive the equation governing the time evolution of the 'unnormahzed' form of the conditional expectation, and express its solution as a multiple integral expansion whose existence is guaranteed by Wiener's theorem. The usual 'signal plus noise' model is a special case of the situation studied here.

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