Matches in SemOpenAlex for { <https://semopenalex.org/work/W2092187622> ?p ?o ?g. }
Showing items 1 to 57 of
57
with 100 items per page.
- W2092187622 endingPage "1001" @default.
- W2092187622 startingPage "981" @default.
- W2092187622 abstract "With z. a signal process, w. a Brownian motion, and y <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>t</inf> = ∫ <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</inf> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>t</sup> z <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>s</inf> ds + w <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>t</inf> , a noisy observation, the innovations problem is to determine whether y. is adapted to the innovations process v., which is also a Brownian motion, and is defined using the estimate <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$hat {z}_t = E{z_{t}vert y_{s}, 0 leq s leq t}$</tex> by <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$y_{t} = ∫_{0}^{t} hat {z}_{s}ds + v_{t}$</tex> . The closely related σ-algebras problem in stochastic DEs is to determine, for a given causal drift α, when a solution of dξ = α(t, ξ)dt + dw is a causal functional of w. Previous results on these problems are reviewed and extended. In particular, we broach and answer positively the physically important case of the innovations problem in which the signal satisfies a stochastic de with drift depending in part on the noisy observations. This case is important because it models a system observed through noise and controlled by feedback of these noisy observations. The last part of the paper shows that the innovations problem has a positive resolution if and only if on some probability space there is a Brownian motion W and a causal solution ξ of dξ = α(t, ξ)dt + dW, where α expresses the estimator <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$hat z;$</tex> that is, α is a causal functional such that <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$hat z_{t} = α(t, y)$</tex> ." @default.
- W2092187622 created "2016-06-24" @default.
- W2092187622 creator A5017930653 @default.
- W2092187622 date "1976-09-01" @default.
- W2092187622 modified "2023-09-25" @default.
- W2092187622 title "On Kailath's Innovations Conjecture Hold" @default.
- W2092187622 cites W108479084 @default.
- W2092187622 cites W197004298 @default.
- W2092187622 cites W2001536360 @default.
- W2092187622 cites W2003922224 @default.
- W2092187622 cites W2044833311 @default.
- W2092187622 doi "https://doi.org/10.1002/j.1538-7305.1976.tb02924.x" @default.
- W2092187622 hasPublicationYear "1976" @default.
- W2092187622 type Work @default.
- W2092187622 sameAs 2092187622 @default.
- W2092187622 citedByCount "6" @default.
- W2092187622 countsByYear W20921876222015 @default.
- W2092187622 countsByYear W20921876222019 @default.
- W2092187622 crossrefType "journal-article" @default.
- W2092187622 hasAuthorship W2092187622A5017930653 @default.
- W2092187622 hasConcept C105795698 @default.
- W2092187622 hasConcept C112401455 @default.
- W2092187622 hasConcept C11413529 @default.
- W2092187622 hasConcept C114614502 @default.
- W2092187622 hasConcept C154945302 @default.
- W2092187622 hasConcept C2780990831 @default.
- W2092187622 hasConcept C33923547 @default.
- W2092187622 hasConcept C41008148 @default.
- W2092187622 hasConceptScore W2092187622C105795698 @default.
- W2092187622 hasConceptScore W2092187622C112401455 @default.
- W2092187622 hasConceptScore W2092187622C11413529 @default.
- W2092187622 hasConceptScore W2092187622C114614502 @default.
- W2092187622 hasConceptScore W2092187622C154945302 @default.
- W2092187622 hasConceptScore W2092187622C2780990831 @default.
- W2092187622 hasConceptScore W2092187622C33923547 @default.
- W2092187622 hasConceptScore W2092187622C41008148 @default.
- W2092187622 hasIssue "7" @default.
- W2092187622 hasLocation W20921876221 @default.
- W2092187622 hasOpenAccess W2092187622 @default.
- W2092187622 hasPrimaryLocation W20921876221 @default.
- W2092187622 hasRelatedWork W1506619093 @default.
- W2092187622 hasRelatedWork W1645173339 @default.
- W2092187622 hasRelatedWork W2555640012 @default.
- W2092187622 hasRelatedWork W2910562253 @default.
- W2092187622 hasRelatedWork W2994753695 @default.
- W2092187622 hasRelatedWork W3119737209 @default.
- W2092187622 hasRelatedWork W3126958331 @default.
- W2092187622 hasRelatedWork W3160974663 @default.
- W2092187622 hasRelatedWork W4224131443 @default.
- W2092187622 hasRelatedWork W4225848310 @default.
- W2092187622 hasVolume "55" @default.
- W2092187622 isParatext "false" @default.
- W2092187622 isRetracted "false" @default.
- W2092187622 magId "2092187622" @default.
- W2092187622 workType "article" @default.