We study the estimation of moments and joint moments of microstructure noise. Estimators of arbitrary order of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide estimators of auto-covariances and auto-correlations of the noise. Simulation studies demonstrate excellent performance of our estimators even in the presence o...

Twenty young healthy adults walked and crossed obstacles of heights of 10%, 20% and 30% of their leg lengths and kinematics and kinetics of their gait analysed. Three-dimensional joint moments of the lower limb were calculated with inverse dynamics analysis. Peak moments and crossing moments (joint moments at the time when the swing foot is above the obstacle) were obtained. Most of the peak mo...

We introduce a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions. The idea is to write the distribution fonction f in all its domain as the sum of a Maxwellian adapted to the boundary (which is not the usual Maxwellian associated with f) and a reminder kinetic part. This Maxwellian is defined such that its ’incoming’ ...