From Nonparametric Regression to Statistical Inference for Non-Ergodic Diffusion Processes

This book is about copies-based nonparametric estimation of the drift function in stochastic differential equations (SDEs) driven by Brownian motion, a jump process, or fractional Brownian motion. While the estimators of the drift function in SDEs are classically computed from one long-time observation of the ergodic stationary solution, here the estimation framework – which is part of functional data analysis – involves multiple copies of the (non-stationary) solution observed over a short...