819 research outputs found
A Variation Embedding Theorem and Applications
Fractional 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
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