Stochastic inequalities constitute a fundamental building block of Probability Theory. On the other hand, they form a major thread within and between various subareas of Probability and Statistics. Examples of such inequalities that have experienced a recent development and have produced an impact on different areas are the following ones:
- Concentration and deviation inequalities for various types of stochastic processes. The recent breakthrough of Talagrand showing that the supremum of an empirical process concentrates about its mean with very large probability has been applied in many areas of Statistics, like model selection, density estimation and survival analysis;
- Estimation of the p norms of sums of independent random variables in terms of the individual distributions of the summands.
- Inequalities in Malliavin calculus and its applications to density estimates and to estimates for anticipating integrals;
- Geometric inequalities for log-concave probability measures. The recent progress in the correlation inequality for Gaussian measures has been applied to the computation of Onsager-Machlup functionals for solutions of stochastic partial differential equations and diffusion processes;
- Further advances in martingale inequalities have been applied to the geometry of Banach spaces and decoupling inequalities have been successfully applied in the asymptotic theory of U-statistics and multilinear forms.
This conference will provide a unique opportunity for collaboration and exchange of ideas between probabilists working in stochastic inequalities and other researchers that are using estimates based on stochastic inequalities in different fields of Probability Theory and Statistics.
In particular space will be provided in the afternoon sessions for less established young researchers and students, to interact with the most experienced ones, including lecturers and keynote speakers. Two afternoons will be devoted to this objective in problem sessions and discussions plus an afternoon free of talks to facilitate contacts.