A Variation Embedding Theorem and Applications

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dc.creatorFriz, Peter
dc.creatorVictoir, Nicolas
dc.date2005-11-21
dc.date.accessioned2026-07-07T06:51:32Z
dc.date.available2026-07-07T06:51:32Z
dc.descriptionFractional Sobolev spaces, also known as Besov or Slobodetzki spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces and discuss a few applications. First we show q-variation regularity of Cameron-Martin paths associated to fractional Brownian motion and other Volterra processes. This is useful, for instance, to establish large deviations for enhanced fractional Brownian motion. Second, the q-variation embedding, combined with results of rough path theory, provides a different route to a regularity result for stochastic differential equations by Kusuoka. Third, the embedding theorem works in a non-commutative setting and can be used to establish Hoelder/variation regularity of rough paths.
dc.identifierhttps://arxiv.org/abs/math/0511520
dc.identifierhttp://arxiv.org/abs/math/0511520
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105018
dc.subjectProbability
dc.subjectFunctional Analysis
dc.subject60H99; 60G17
dc.titleA Variation Embedding Theorem and Applications
dc.typetext

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