Locally Perturbed Random Walks

This monograph provides a comprehensive overview of locally perturbed random walks, tools used for their analysis, and current research on their applications. The authors present the material in a self-contained manner, providing strong motivation in Chapter One with illustrative examples of locally perturbed random walks and an introduction of the mathematical tools that are used throughout the book. Chapter Two shows the construction of various stochastic processes that serve as scaling limits for locally perturbed random walks, particularly focusing on reflected and skewed processes. In Chapter Three, the authors prove various limit theorems for these perturbed random walks. The final chapter serves as an appendix that collects essential background material for readers who wish to understand the arguments more deeply. Locally Perturbed Random Walks will appeal to researchers interested in this area within modern probability theory. It is also accessible to students who have taken a second course in probability.