Vidyadhar Mandrekar Livres

Utilizing Poisson random measures, this book presents a novel approach to modeling complex systems influenced by random sources, such as financial interest rates and temperature variations. It explores the solutions of stochastic differential equations, focusing on their long-term behavior and sensitivity to initial conditions. The authors delve into integration theory within Banach spaces, extending beyond the typical Gaussian frameworks. Aimed at graduate students and researchers, it requires a solid understanding of stochastic processes, probability, and functional analysis.

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,∞) Central limit theorem for semi-martingales and applications Central limit theorems for dependent random variables Empirical process Bibliography