Linear transformation of quasi-invariant measures

Nonexistence of Quasi-invariant Measures on Infinite-dimensional Linear Spaces1

It was shown by V. N. Sudakov [7] that a locally convex topological linear space with a nontrivial quasi-invariant <r-finite measure on its weakly measurable sets must be finite-dimensional. Sudakov's ingenious proof uses a theorem of Ulam [6, Footnote 3]. In some unpublished notes [8], Y. Umemara attempted to prove the same theorem, by utilizing Weil's "converse to the existence of Haar measur...

Admissible vector fields and quasi-invariant measures∗

Quasi-Monte Carlo in the Parallel Computation of Invariant Measures

For a non-singular multi-dimensional mapping S: X Æ X, the corresponding FrobeniusPerron operator is P. In the paper, the schemes for generating the quasi-random numbers are studied for the parallel computation for the fixed density of P. The numerical results for these schemes are presented.

Parallel Quasi-Monte Carlo Computation of Invariant Measures

where m is the Lebesgue measure of R, has a fixed density f∗. This fixed density gives rise to a physical measure of S, which describes the asymptotic behavior of the chaotic orbits from the statistical viewpoint [3]. Our purpose is efficient computation of such fixed densities. In his book [6], Ulam proposed a piecewise constant approximation method to calculate the fixed density f∗ and conjec...

Quasi-invariant measures on the path space of a diffusion

The author has previously constructed a class of admissible vector fields on the path space of an elliptic diffusion process x taking values in a closed compact manifold. In this Note the existence of flows for this class of vector fields is established and it is shown that the law of x is quasi-invariant under these flows. Résumé L’auteur a précédemment construit une classe de champs de vecteu...