{"?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-8K3A5WIZ/21faf77185d77fad2ca0854e8--c-9-b8f5e/PDF","dcterms:extent":"326 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-8K3A5WIZ/177ebf27-5f8e-4c89-802d-a5d1fa57c8af/TEXT","dcterms:extent":"19 KB"}],"edm:TimeSpan":{"@rdf:about":"2014-2024","edm:begin":{"@xml:lang":"en","#text":"2014"},"edm:end":{"@xml:lang":"en","#text":"2024"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-8K3A5WIZ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-OE00UKYR"},{"@xml:lang":"sl","#text":"Matrika"}],"dcterms:issued":"2024","dc:creator":"Rozman, Anej","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"10 str."},{"@xml:lang":"sl","#text":"letnik:11"}],"dc:identifier":["COBISSID_HOST:190005507","ISSN:2385-8567","URN:URN:NBN:SI:doc-8K3A5WIZ"],"dc:language":"sl","dc:publisher":{"@xml:lang":"sl","#text":"Založba Fakultete za matematiko in fiziko Univerze v Ljubljani"},"dc:subject":[{"@xml:lang":"en","#text":"Brownian motion"},{"@xml:lang":"sl","#text":"Brownovo gibanje"},{"@xml:lang":"sl","#text":"krepka lastnost Markova"},{"@xml:lang":"sl","#text":"matematični opis"},{"@xml:lang":"en","#text":"mathematical definition"},{"@xml:lang":"sl","#text":"neodvedljivost"},{"@xml:lang":"en","#text":"non-differentiability"},{"@xml:lang":"en","#text":"random processes"},{"@xml:lang":"en","#text":"reflection"},{"@xml:lang":"sl","#text":"slučajni procesi"},{"@xml:lang":"en","#text":"strong Markov property"},{"@xml:lang":"sl","#text":"šibka lastnost Markova"},{"@xml:lang":"en","#text":"weak Markov property"},{"@xml:lang":"sl","#text":"zrcaljenje"}],"dcterms:temporal":{"@rdf:resource":"2014-2024"},"dc:title":{"@xml:lang":"sl","#text":"Brownovo gibanje|"},"dc:description":[{"@xml:lang":"sl","#text":"In this paper we motivate the idea of Brownian motion and give its mathematical definition. We define basic concepts such as a stochastic process, sample path, increment, filtration and stopping time. We present and prove some basic properties and results, such as the symmetry of Brownian motion, weak Markov property, strong Markov property, reflection principle and the surprising result that the sample path of Brownian motion is nowhere differentiable"},{"@xml:lang":"sl","#text":"V članku motiviramo idejo Brownovega gibanja in podamo njegovo matematično definicijo. Definiramo osnovne pojme, kot so slučajni proces, trajektorija, prirastek, filtracija in čas ustavljanja. Predstavimo in dokažemo nekaj osnovnih lastnosti ter rezultatov, kot je simetričnost Brownovega gibanja, šibka lastnost Markova, krepka lastnost Markova, princip zrcaljenja in presenetljiv rezultat, da je trajektorija Brownovega gibanja neodvedljiva funkcija"}],"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-8K3A5WIZ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-8K3A5WIZ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-8K3A5WIZ/21faf77185d77fad2ca0854e8--c-9-b8f5e/PDF"},"edm:rights":{"@rdf:resource":"http://rightsstatements.org/vocab/InC/1.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:dataProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-8K3A5WIZ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-8K3A5WIZ"}}}}