{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-FXRL3RVN/e66386f3-6a8c-4fa3-a830-371beec8d25d/PDF","dcterms:extent":"402 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-FXRL3RVN/99e6d7b5-a25b-40cb-8001-3826aa001b87/TEXT","dcterms:extent":"31 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-FXRL3RVN","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2016","dc:creator":"Gajser, David","dc:format":[{"@xml:lang":"sl","#text":"letnik:10"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 393-410"}],"dc:identifier":["COBISSID:17736025","ISSN:1855-3966","URN:URN:NBN:SI:doc-FXRL3RVN"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"binomial mean"},{"@xml:lang":"sl","#text":"binomska sredina"},{"@xml:lang":"en","#text":"Cesaro mean"},{"@xml:lang":"sl","#text":"Cesarova sredina"},{"@xml:lang":"en","#text":"convergence"},{"@xml:lang":"en","#text":"finite Markov chain"},{"@xml:lang":"sl","#text":"končna Markovska veriga"},{"@xml:lang":"sl","#text":"konvergenca"},{"@xml:lang":"en","#text":"sequence"},{"@xml:lang":"sl","#text":"zaporedje"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On convergence of binomial means, and an application to finite Markov chains|"},"dc:description":[{"@xml:lang":"sl","#text":"For a sequence ?$\\{a_n\\}_{n \\ge 0}$? of real numbers, we define the sequence of its arithmetic means ?$\\{a_n^\\ast\\}_{n \\ge 0}$? as the sequence of averages of the first ?$n$? elements of ?$\\{a_n\\}_{n \\ge 0}$?. For a parameter ?$0 < p < 1$?, we define the sequence of ?$p$?-binomial means ?$\\{a_n^p\\}_{n \\ge 0}$? of the sequence ?$\\{a_n\\}_{n \\ge 0}$? as the sequence of ?$p$?-binomially weighted averages of the first ?$n$? elements of ?$\\{a_n\\}_{n \\ge 0}$?. We compare the convergence of sequences ?$\\{a_n\\}_{n \\ge 0}$?, ?$\\{a_n^\\ast\\}_{n \\ge 0}$? and ?$\\{a_n^p\\}_{n \\ge 0}$? for various ?$0 < p < 1$?, i.e., we analyze when the convergence of one sequence implies the convergence of the other. While the sequence ?$\\{a_n^\\ast\\}_{n \\ge 0}$?, known also as the sequence of Cesaro means of a sequence, is well studied in the literature, the results about ?$\\{a_n^p\\}_{n \\ge 0}$? are hard to find. Our main result shows that, if ?$\\{a_n\\}_{n \\ge 0}$? is a sequence of non-negative real numbers such that ?$\\{a_n^p\\}_{n \\ge 0}$? converges to ?$a \\in \\mathbb{R} \\cup \\{\\infty\\}$? for some ?$0 < p < 1$, then $\\{a_n^p\\}_{n \\ge 0}$? also converges to ?$a$?. We give an application of this result to finite Markov chains"},{"@xml:lang":"sl","#text":"Za zaporedje ?$\\{a_n\\}_{n \\ge 0}$? realnih števil definiramo zaporedje njegovih aritmetičnih sredin ?$\\{a_n^\\ast\\}_{n \\ge 0}$? kot zaporedje povprečij prvih ?$n$? členov zaporedja ?$\\{a_n\\}_{n \\ge 0}$?. Za parameter ?$0 < p < 1$? definiramo zaporedje ?$p$?-binomskih sredin ?$\\{a_n^p\\}_{n \\ge 0}$? zaporedja ?$\\{a_n\\}_{n \\ge 0}$? kot zaporedje ?$p$?-binomsko uteženih povprečij prvih ?$n$? členov zaporedja ?$\\{a_n\\}_{n \\ge 0}$?. Primerjamo konvergenco zaporedij ?$\\{a_n\\}_{n \\ge 0}$?, ?$\\{a_n^\\ast\\}_{n \\ge 0}$? in ?$\\{a_n^p\\}_{n \\ge 0}$? za različne ?$0 < p < 1$? oziroma analiziramo, kdaj konvergenca enega zaporedja implicira konvergenco drugega. Medtem ko je zaporedje ?$\\{a_n^\\ast\\}_{n \\ge 0}$?, znano tudi kot zaporedje Cesarovih sredin zaporedja, dobro raziskano v literaturi, pa je rezultate v zvezi z ?$\\{a_n^p\\}_{n \\ge 0}$? težko najti. Naš glavni rezultat pokaže, da če je ?$\\{a_n\\}_{n \\ge 0}$? zaporedje nenegativnih realnih števil in ?$\\{a_n^p\\}_{n \\ge 0}$? konvergira k ?$a \\in \\mathbb{R} \\cup \\{\\infty\\}$? za neki ?$0 < p < 1$?, potem ?$\\{a_n^\\ast\\}_{n \\ge 0}$? prav tako konvergira k ?$a$?. Podamo aplikacijo tega rezultata v končnih Markovskih verigah"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-FXRL3RVN","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-FXRL3RVN"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-FXRL3RVN/e66386f3-6a8c-4fa3-a830-371beec8d25d/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-FXRL3RVN/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-FXRL3RVN"}}}}