P-variation (original) (raw)
In mathematical analysis, p-variation is a collection of seminorms on functions from an ordered set to a metric space, indexed by a real number . p-variation is a measure of the regularity or smoothness of a function. Specifically, if , where is a metric space and I a totally ordered set, its p-variation is where D ranges over all finite partitions of the interval I. The p variation of a function decreases with p. If f has finite p-variation and g is an α-Hölder continuous function, then has finite -variation.
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| dbo:abstract | In mathematical analysis, p-variation is a collection of seminorms on functions from an ordered set to a metric space, indexed by a real number . p-variation is a measure of the regularity or smoothness of a function. Specifically, if , where is a metric space and I a totally ordered set, its p-variation is where D ranges over all finite partitions of the interval I. The p variation of a function decreases with p. If f has finite p-variation and g is an α-Hölder continuous function, then has finite -variation. The case when p is one is called total variation, and functions with a finite 1-variation are called bounded variation functions. (en) |
| dbo:wikiPageExternalLink | http://web.sgh.waw.pl/~rlocho/UCT_talk.pdf https://fabricebaudoin.wordpress.com/2012/12/24/lecture-6-continuous-paths-with-bounded-p-variation/ |
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| dbo:wikiPageWikiLink | dbr:Big-O_notation dbr:Bounded_variation dbr:Mathematical_analysis dbr:Norm_(mathematics) dbr:Dynamic_programming dbr:Partition_of_an_interval dbc:Mathematical_analysis dbr:Wiener_process dbr:Hölder_continuous dbr:Metric_space dbr:Total_variation dbr:Quadratic_variation dbr:Rough_path dbr:Riemann–Stieltjes_Integral dbr:Stochastic_analysis |
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| rdfs:comment | In mathematical analysis, p-variation is a collection of seminorms on functions from an ordered set to a metric space, indexed by a real number . p-variation is a measure of the regularity or smoothness of a function. Specifically, if , where is a metric space and I a totally ordered set, its p-variation is where D ranges over all finite partitions of the interval I. The p variation of a function decreases with p. If f has finite p-variation and g is an α-Hölder continuous function, then has finite -variation. (en) |
| rdfs:label | P-variation (en) |
| owl:sameAs | wikidata:P-variation https://global.dbpedia.org/id/4YFnb |
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| is dbo:wikiPageWikiLink of | dbr:Total_variation dbr:Variation dbr:Quadratic_variation |
| is foaf:primaryTopic of | wikipedia-en:P-variation |