879,494 research outputs found
Sample Path Properties of Bifractional Brownian Motion
Let be a bifractional
Brownian motion in . We prove that is strongly locally
nondeterministic. Applying this property and a stochastic integral
representation of , we establish Chung's law of the iterated
logarithm for , as well as sharp H\"older conditions and tail
probability estimates for the local times of . We also consider the
existence and the regularity of the local times of multiparameter bifractional
Brownian motion in using Wiener-It\^o chaos expansion
Limits of bifractional Brownian noises
Let be a bifractional Brownian motion with
two parameters and . The main result of this paper is
that the increment process generated by the bifractional Brownian motion
converges when to
, where is the
fractional Brownian motion with Hurst index . We also study the behavior of
the noise associated to the bifractional Brownian motion and limit theorems to
The group of homeomorphisms of the Cantor set has ample generics
We show that the group of homeomorphisms of the Cantor set has ample
generics, that is, for every the diagonal conjugacy action
of on
has a comeager orbit. This answers a question of Kechris and Rosendal.
We show that the generic tuple in can be taken to be the limit of a
certain projective Fraisse family. We also present a proof of the existence of
the generic homeomorphism of the Cantor set in the context of the projective
Fraisse theory.Comment: final version, to appear in Bulletin of the London Mathematical
Societ
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