Nearest-neighbour modelling of reciprocal chains (Articolo in rivista)

Type
Label
  • Nearest-neighbour modelling of reciprocal chains (Articolo in rivista) (literal)
Anno
  • 2008-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1080/17442500802088517 (literal)
Alternative label
  • Carravetta, F. (2008)
    Nearest-neighbour modelling of reciprocal chains
    in Stochastics (Abingdon. Print); Taylor & Francis Group, London (Regno Unito)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Carravetta, F. (literal)
Pagina inizio
  • 525 (literal)
Pagina fine
  • 584 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://www.tandf.co.uk/journals/journal.asp?issn=1744-2508&linktype=1 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 80 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#note
  • La rivista, storicamente nota come 'Stochastics', ha modificato il proprio nome in: 'Stochastics: an international journal of probability and stochastic processes' (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
  • 59 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 6 (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Istituto di Analisi dei Sistemi ed Informatica 'A. Ruberti', Consiglio Nazionale delle Ricerche, Viale Manzoni 30, Rome 00185, Italy (literal)
Titolo
  • Nearest-neighbour modelling of reciprocal chains (literal)
Abstract
  • This paper focuses on the class of finite-state, discrete-index, reciprocal processes (reciprocal chains). Such a class of processes seems to be a suitable setup in many applications and, in particular, it appears well-suited for image-processing. While addressing this issue, the aim is 2-fold: theoretic and practical. As to the theoretic purpose, some new results are provided: first, a general stochastic realization result is provided for reciprocal chains endowed with a known, arbitrary, distribution. Such a model has the form of a fixed-degree, nearest-neighbour polynomial model. Next, the polynomial model is shown to be exactly linearizable, which means it is equivalent to a nearest-neighbour linear model in a different set of variables. The latter model turns out to be formally identical to the Levi-Frezza-Krener linear model of a Gaussian reciprocal process, although actually non-linear with respect to the chain's values. As far as the practical purpose is concerned, in order to yield an example of application an estimation issue is addressed: a suboptimal (polynomial-optimal) solution is derived for the smoothing problem of a reciprocal chain partially observed under non-Gaussian noise. To this purpose, two kinds of boundary conditions (Dirichlet and Cyclic), specifying the reciprocal chain on a finite interval, are considered, and in both cases the model is shown to be well-posed, in a 'wide-sense'. Under this view, some well-known representation results about Gaussian reciprocal processes extend, in a sense, to a 'non-Gaussian' case. (literal)
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