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New characterizations for wide-sense Markov signals which are based either on second-order properties or on state-space representations are studied in a widely linear setting. Moreover, the correlation structure of such signals is revealed and interesting results on modeling in both the forwards and backwards time directions are proved. As an application we give some recursive estimation algorithms obtained from the Kalman filter. The performance of the proposed results is illustrated in a numerical example in the areas of estimation and simulation.<\/jats:p>","DOI":"10.1186\/1687-6180-2012-256","type":"journal-article","created":{"date-parts":[[2012,12,18]],"date-time":"2012-12-18T11:14:28Z","timestamp":1355829268000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Widely linear Markov signals"],"prefix":"10.1186","volume":"2012","author":[{"given":"Juan A","family":"Espinosa-Pulido","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jes\u00fas","family":"Navarro-Moreno","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rosa M","family":"Fern\u00e1ndez-Alcal\u00e1","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan C","family":"Ruiz-Molina","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,12,18]]},"reference":[{"key":"412_CR1","volume-title":"Linear Estimation","author":"T Kailath","year":"2000","unstructured":"Kailath T, Sayed AH, Hassibi B: Linear Estimation. 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