Refinements of the One Dimensional Free Poincare Inequality
We present two extensions of the one dimensional free Poincaré inequality similar in spirit to two classical refinements.
math.PR↗
arXiv subjects
Christian Houdre
Publications and source records attributed to Christian Houdre.
Nonparametric estimation for Levy processes with a view towards mathematical finance
Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model selection approach made up of two steps is investigated. The first step consists in the selection of a good estimator from a linear model of proposed Levy densities, while the second is a data-driven selection of a linear model among a given collection of linear models. By providing lower bounds for the minimax risk of estimation over Besov Levy densities, our estimators are shown to achieve the ``best'' rate of convergence. A numerical study for the case of histogram estimators and for variance Gamma processes, models of key importance in risky asset price modeling driven by Levy processes, is presented.
math.ST↗
On the concentration of measure phenomenon for stable and related random vectors
Concentration of measure is studied, and obtained, for stable and related random vectors.
math.PR↗