An extreme absolutely continuous ${\rm RP}$-measure

Exchangeable Sequences Driven by an Absolutely Continuous Random Measure

Let S be a Polish space and (Xn : n ≥ 1) an exchangeable sequence of S-valued random variables. Let αn(·) = P ( Xn+1 ∈ · | X1, . . . , Xn ) be the predictive measure and α a random probability measure on S such that αn weak −→ α a.s.. Two (related) problems are addressed. One is to give conditions for α λ a.s., where λ is a (non random) σ-finite Borel measure on S. Such conditions should concer...

NONINVERTIBLE TRANSFORMATIONS ADMITTING NO ABSOLUTELY CONTINUOUS ct-FINITE INVARIANT MEASURE

We study a family of H-to-1 conservative ergodic endomorphisms which we will show to admit no rj-finite absolutely continuous invariant measure. We exhibit recurrent measures for these transformations and study their ratio sets; the examples can be realized as C°° endomorphisms of the 2-torus.

No-arbitrage conditions and absolutely continuous changes of measure

We study the stability of several no-arbitrage conditions with respect to absolutely continuous, but not necessarily equivalent, changes of measure. We rst consider models based on continuous semimartingales and show that no-arbitrage conditions weaker than NA and NFLVR are always stable. Then, in the context of general semimartingale models, we show that an absolutely continuous change of meas...

On Absolutely Continuous Transformations

Non-absolutely Continuous Foliations

We consider a partially hyperbolic diffeomorphism of a compact smooth manifold preserving a smooth measure. Assuming that the central distribution is integrable to a foliation with compact smooth leaves we show that this foliation fails to have the absolute continuity property provided that the sum of Lyapunov exponents in the central direction is not zero on a set of positive measure. We also ...