Curs 2017-2018: Abstracts i Slides



16/05/18:  Jorge León, CINVESTAV, México.

Ecuaciones diferenciales fraccionarias gobernadas por un ruido $\gamma$-Holder continuo con $\gamma>1/2$

En esta charla estudiaremos la existencia de una única solución para ecuaciones diferenciales fraccionarias semilineales en el sentido de Young gobernadas por un ruido $\gamma$-Holder continuo, con $\gamma>1/2$. La condición inicial $\xi$ puede ser una función Holder continua o la función $t\mapsto t^\alpha\xi_t$ puede ser Holder continua, para algún $\alpha\in(0,1)$.


11/04/2018:  Elisa Alòs, Universitat Pompeu Fabra, Barcelona.

The asymptotic expansion of the regular discretization error of Ito integrals.

We study a Edgeworth-type refinement of the central limit theorem for the discretizacion error of Itô integrals. Towards this end, we introduce a new approach, based on the anticipating Itô formula. This alternative technique allows us to compute explicitly the terms of the corresponding expansion formula. This is joint work with M. Fukasawa, Osaka University.

29/11/2017:  Robert Dalang, Ecole Polytechnique Fédérale de Lausanne, Switzerland.

Hausdorff dimension of the boundary of Brownian bubbles.

Let $W = (W(s),\, s\in \R^2_+)$ be a standard Brownian sheet indexed by the nonnegative quadrant. We show that with probability one, the Hausdorff dimension of the boundary of any connected component of the random open set $\{(s_1,s_2)\in \R^2_+: W(s_1,s_2) >0\}$ is equal to $ \frac{1}{4}\left(1 + \sqrt{13 + 4 \sqrt{5}}\right) \simeq 1.421\ . $ This result is first established for additive Brownian motion, which provides good local approximations to the Brownian sheet, and then extended, with some technical effort, to the Brownian sheet itself. This is joint work with T.~Mountford (Ecole Polytechnique Fédérale de Lausanne. A preprint is available at