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About: P-variation     Goto   Sponge   NotDistinct   Permalink

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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.