Wavelet Estimation of Deformed Stationary Processes
        Maureen Clerc (CERMICS - ENPC)


We study classes of nonstationary processes, such as warped processes and
frequency-modulated processes, that result from the deformation of
stationary processes. Estimating the deformation can often provide
important information about an underlying physical process. With a
computational harmonic analysis viewpoint, we show that the deformed
autocovariance satisfies a transport equation at small scales, with a
velocity equal to the gradient of the deformation. We derive an estimator
for the deformation from one realization of the deformed process, and we
prove its consistency under appropriate assumptions.