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 processesWeak convergence in metric spacesWeak convergence on C[0, 1] and D[0,∞)Central limit theorem for semi-martingales and applicationsCentral limit theorems for dependent random variablesEmpirical processBibliography.

• Contents
• 1. Weak convergence of stochastic processes
• 2. Weak convergence in metric spaces
• 3. Weak convergence on C[0, 1] and D[0,8)
• 4. Central limit theorem for semi-martingales and applications
• 5. Central limit theorems for dependent random variables
• 6. Empirical process
• Bibliography