Théorie spectrale d'un opérateur de transition sur un espace métrique compact
The last few years have witnessed important new developments in the theory and practice of pattern classification. We intend to survey some of the main new ideas that have led to these recent results.
The last few years have witnessed important new developments in the theory and practice of pattern classification. We intend to survey some of the main new ideas that have led to these recent results.
Optimization problems depending on a probability measure correspond to many applications. These problems can be static (single-stage), dynamic with finite (multi-stage) or infinite horizon, single- or multi-objective. It is necessary to have complete knowledge of the “underlying” probability measure if we are to solve the above-mentioned problems with precision. However this assumption is very rarely fulfilled (in applications) and consequently, problems have to be solved mostly on the basis of...
In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. ) and equations of type.
We prove that for s < 0, s-concave measures on ℝⁿ exhibit thin-shell concentration similar to the log-concave case. This leads to a Berry-Esseen type estimate for most of their one-dimensional marginal distributions. We also establish sharp reverse Hölder inequalities for s-concave measures.
We show that the only flow solving the stochastic differential equation (SDE) on
Some sufficient conditins for tightness of continuous stochastic processes is given. It is verified that in the classical tightness sufficient conditions for continuous stochastic processes it is possible to take a continuous nondecreasing stochastic process instead of a deterministic function one.