1,373 research outputs found
Stochastic Equivariant Cohomologies and Cyclic Cohomology
We give two stochastic diffeologies on the free loop space which allow us to
define stochastic equivariant cohomology theories in the Chen-Souriau sense and
to establish a link with cyclic cohomology. With the second one, we can
establish a stochastic fixed point theorem.Comment: Published at http://dx.doi.org/10.1214/009117905000000170 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Sensitivity Analysis for Convex Multiobjective Programming in Abstract Spaces.
The main object of this paper is to prove that for a linear or convex multiobjective program, a dual program can be obtained which gives the primal sensitivity without any special hypothesis about the way of choosing the optimal solution in the efficient set.
Bifurcation of Fredholm Maps I; The Index Bundle and Bifurcation
We associate to a parametrized family of nonlinear Fredholm maps
possessing a trivial branch of zeroes an {\it index of bifurcation}
which provides an algebraic measure for the number of bifurcation points from
the trivial branch. The index is derived from the index bundle of
the linearization of the family along the trivial branch by means of the
generalized -homomorphism. Using the Agranovich reduction and a
cohomological form of the Atiyah-Singer family index theorem, due to Fedosov,
we compute the bifurcation index of a multiparameter family of nonlinear
elliptic boundary value problems from the principal symbol of the linearization
along the trivial branch. In this way we obtain criteria for bifurcation of
solutions of nonlinear elliptic equations which cannot be achieved using the
classical Lyapunov-Schmidt method.Comment: 42 pages. Changes: added Lemma 2.31 and a reference + minor
corrections. To appear on TMN
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