A variation embedding theorem and applications |
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Authors: | Peter Friz Nicolas Victoir |
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Institution: | a Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, UK |
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Abstract: | Fractional Sobolev spaces, also known as Besov or Slobodetski spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces. Applications include a new route to a regularity result by Kusuoka for stochastic differential equations, integration against Besov-paths, a regularity criterion for rough paths and a new regularity result for Cameron-Martin paths associated to fractional Brownian motion. |
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Keywords: | Fractional Sobolev Besov spaces q-Variation embedding Rough paths Regularity of the Ito-map Regularity of Cameron-Martin |
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