ISSN:
1572-929X
Keywords:
Stochastic differential equations
;
stochastic flows on manifolds
;
linear cocycles
;
multiplicative ergodic theory
;
Lyapunov exponents
;
Hörmander's theorem
;
Malliavin's calculus.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The Oseledets spaces of a random dynamical system generated by a linear stochastic differential equation are obtained as intersections of the corresponding nested invariant spaces of a forward and a backward flag, described as the stationary states of flows on corresponding flag manifolds. We study smoothness of their laws and conditional laws by applying Malliavin's calculus. If the Lie algebras induced by the actions of the matrices generating the system on the manifolds span the tangent spaces at any point, laws and conditional laws are seen to be C∞-smooth. As an application we find that the semimartingale property is well preserved if the Wiener filtration is enlarged by the information present in the flag or Oseledets spaces.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008680717092
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