دانلود کتاب از رگرسیون ناپارامتری تا استنتاج آماری برای فرآیندهای انتشار غیر ارگودیک

Stochastic Differential Equations (SDEs) are very popular in applications, and statis-tical inference for these models has been an intensively investigated research field for many years. On estimators computed from one long-time observation of the ergodic stationary solution of an SDE, there are already famous books, such as Kutoyants [1] (for diffusions) and Kubilius et al. [2] (for fractional diffusions). However, to my knowledge, there is no book on copies-based statistical inference for such models, which is related to functional data analysis. So, following a presen-tation on this topic to my colleagues at the Modal’X Department of Paris Nanterre University, I decided to write the present book on the projection least squares and Nadaraya-Watson estimators of the drift function computed from multiple short-time observations of an SDE solution. The main purpose of this book is to show to the reader how to extend proof techniques from nonparametric regression to the copies-based estimation of the drift function for various usual models: SDEs driven by Brownian motion, a Lévy process or fractional Brownian motion. The story doesn’t stop there, because I’m already working on a second book on copies-based nonpara-metric estimators of the drift function for more complicated models, and of the transition density function for diffusion processes. Anyway, I hope this first book will help the reader to become familiar with copies-based statistical inference for SDE models.