3,053 research outputs found
Stochastic Shell Models driven by a multiplicative fractional Brownian--motion
We prove existence and uniqueness of the solution of a stochastic
shell--model. The equation is driven by an infinite dimensional fractional
Brownian--motion with Hurst--parameter , and contains a
non--trivial coefficient in front of the noise which satisfies special
regularity conditions. The appearing stochastic integrals are defined in a
fractional sense. First, we prove the existence and uniqueness of variational
solutions to approximating equations driven by piecewise linear continuous
noise, for which we are able to derive important uniform estimates in some
functional spaces. Then, thanks to a compactness argument and these estimates,
we prove that these variational solutions converge to a limit solution, which
turns out to be the unique pathwise mild solution associated to the
shell--model with fractional noise as driving process.Comment: 23 page
Large Deviation Principle for Enhanced Gaussian Processes
We study large deviation principles for Gaussian processes lifted to the free
nilpotent group of step N. We apply this to a large class of Gaussian processes
lifted to geometric rough paths. A large deviation principle for enhanced
(fractional) Brownian motion, in Hoelder- or modulus topology, appears as
special case.Comment: minor corrections; this version to appear in Annales de l'I.H.
L\'evy-areas of Ornstein-Uhlenbeck processes in Hilbert-spaces
In this paper we investigate the existence and some useful properties of the
L\'evy areas of Ornstein-Uhlenbeck processes associated to Hilbert-space-valued
fractional Brownian-motions with Hurst parameter . We prove
that this stochastic area has a H\"older-continuous version with sufficiently
large H\"older-exponent and that can be approximated by smooth areas. In
addition, we prove the stationarity of this area.Comment: 18 page
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