A sequence of real numbers an converges to a limit a if and only if, for each 2 > 0, the sequence an eventually lies within a ball of radius 2 centered at a. It’s okay if the first few (or few million) terms lie outside that ball— and the number of terms that do lie outside the ball may depend on how big 2 is (if 2 is small enough it will take millions of terms before the remaining sequence lie...

– The concept of probability structure preserving mapping is introduced. The idea is applied to define stochastic integral for fractional Brownian motion (fBm) and to obtain an anticipative Girsanov theorem for fBm.  2002 Éditions scientifiques et médicales Elsevier SAS AMS classification: 60H05; 60H07; 60H15; 60B11; 28B20

In this paper we formulate a time-optimal control problem in the space of probability measures. The main motivation is to face situations in nitedimensional control systems evolving deterministically where the initial position of the controlled particle is not exactly known, but can be expressed by a probability measure on R. We propose for this problem a generalized version of some concepts fr...

In the present paper we sketch the proof of the fact that for any open connected set Ω ⊂ Rn+1, n ≥ 1, and any E ⊂ ∂Ω with 0 < H(E) < ∞, absolute continuity of the harmonic measure ω with respect to the Hausdorff measure on E implies that ω|E is rectifiable.

In the present paper we prove that for any open connected set Ω ⊂ R, n ≥ 1, and any E ⊂ ∂Ω with 0 < H(E) < ∞ absolute continuity of the harmonic measure ω with respect to the Hausdorff measure on E implies that ω|E is rectifiable. CONTENTS

Consider a semigroup action on a set. We derive conditions, in terms of the induced action of the semigroup on {0, 1}-valued probability charges, which ensure that all invariant probability charges are strongly continuous.