On estimating a dynamic function of stochastic system with averaging

We consider a two-scaled diffusion system, when drift and diffusion parameters of a 'slow' component are contaminated by an unobservable 'fast' one. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the 'slow' component w.r.t. the stationary distribution of the 'fast' one. For estimation we use a locally linear smoother with a datadriven choice of bandwidth. A procedure proposed is fully adaptive and nearly optimal up to a log log factor. (orig.)Available from TIB Hannover: RR 5549(381) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Deviation probability bound for martingales with applications to statistical estimation

SIGLEAvailable from TIB Hannover: RR 5549(471)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Moderate deviations for integral functionals of diffusion process

Available from TIB Hannover: RR 5549(377) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman