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Peter Imkeller 《Probability Theory and Related Fields》1996,106(1):105-135
Summary. The analytic treatment of problems related to the asymptotic behaviour of random dynamical systems generated by stochastic
differential equations suffers from the presence of non-adapted random invariant measures. Semimartingale theory becomes accessible
if the underlying Wiener filtration is enlarged by the information carried by the orthogonal projectors on the Oseledets spaces
of the (linearized) system.
We study the corresponding problem of preservation of the semimartingale property and the validity of a priori inequalities
between the norms of stochastic integrals in the enlarged filtration and norms of their quadratic variations in case the random
element F enlarging the filtration is real valued and possesses an absolutely continuous law. Applying the tools of Malliavin’s calculus,
we give smoothness conditions on F under which the semimartingale property is preserved and a priori martingale inequalities are valid.
Received: 12 April 1995 / In revised form: 7 March 1996 相似文献
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Knut Smoczyk 《Mathematische Zeitschrift》2002,240(4):849-883
We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive and equal curvature converge to minimal symplectic maps, if the Lagrangian angle for the corresponding Lagrangian submanifold in the cross product space satisfies . If one considers a 4-dimensional K?hler-Einstein manifold of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that is a compact oriented Lagrangian submanifold w.r.t. J such that the K?hler form w.r.t.K restricted to L is positive and , then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. .
Received: 11 April 2001 / Published online: 29 April 2002 相似文献
6.
Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L
2-norm for any u, v∈L
∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that
is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T
-n
A∩S
-
n
A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L
2(X) for all u, v∈L
∞(X) if and only if T×S is ergodic on X×X and the group generated by T
-1
S, T
-2
S
2,..., T
-c
S
c
acts ergodically on X.
Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001 相似文献
7.
Balázs Szendröi 《Mathematische Zeitschrift》2002,240(2):233-241
This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces.
Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002 相似文献
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Nicolas Bergeron 《Mathematische Zeitschrift》2002,241(1):101-125
Let M be an arithmetic hyperbolic manifold and be a codimension 1 geodesic cycle. In this paper, we study the asymptotic growth of the -norm of the lifts of F in the congruence tower above M. We obtain an explicit value for the growth rate of this norm. In particular, we provide a new proof of a celebrated result
of Millson [Mi] on the homology of the arithmetic hyperbolic manifolds. The method is quite general and gives a new way of
getting non zero homology classes in certain locally symmetric spaces.
Received: 20 April 2001; in final form: 26 September 2001 / Published online: 28 February 2002 相似文献