Vidyadhar S. Mandrekar 
Weak Convergence of Stochastic Processes [PDF ebook] 
With Applications to Statistical Limit Theorems

The purpose of this book is to present results on the subject of weak convergence in function spaces to study invariance principles in statistical applications to dependent random variables, U-statistics, censor data analysis. Different techniques, formerly available only in a broad range of literature, are for the first time presented here in a self-contained fashion. Contents:Weak convergence of stochastic processes Weak convergence in metric spaces Weak convergence on C[0, 1] and D[0, infinity)Central limit theorem for semi-martingales and applications Central limit theorems for dependent random variables Empirical process Bibliography