Innovations Informational Equivalence for Observations with Feedback

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  • フィードバックをもつ観測機構に対するイノベーションの情報等価性
  • フィードバック オ モツ カンソク キコウ ニ タイスル イノベーション ノ

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Abstract

The problem of innovations informational equivalence is discussed for observations with feedback. The additive noise is assumed to be a continuous square integrable martingale. Under the assumptions of 1) square integrability on the signal; 2) mutual independence between the noise and the part of the signal other than the feedback; 3) existence and uniqueness of the strong solution of the observation equation as a stochastic differential equation; 4) a weighted square integrability on the signal, it is shown that the innovations informational equivalence holds.

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