Locally Perturbed Random Walks

Erscheinungsjahr 2025
ISBN: 978-3-031-83918-4
Verlag: Springer International Publishing

Buch, Englisch, 248 Seiten, Format (B × H): 168 mm x 240 mm, Gewicht: 449 g

Reihe: Frontiers in Mathematics

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. 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.

Zielgruppe

Research

Autoren/Hrsg.

Iksanov, Alexander

Samoilenko, Ihor

Marynych, Alexander

Pilipenko, Andrey

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Chapter 1: Introduction.- Chapter 2: L´evy-type processes with singularities.- Chapter 3: Functional limit theorems for locally perturbed random walks.- Chapter 4: Auxiliary results.

Über Autor(innen)

Alexander Iksanov is Head of Operations Research Department at Taras Shevchenko National University of Kyiv. Among his main mathematical interests are Discrete Probability Theory and Stochastic Processes.

Alexander Marynych, a Ukrainian mathematician, specializes in stochastic processes and random structures, with research spanning geometry, probability, and number theory.

Andrey Pilipenko is Leading Researcher at the Institute of Mathematics, Ukrainian National Academy of Sciences, and Professor at Igor Sikorsky Kyiv Polytechnic Institute.  Among his main mathematical interests are Stochastic Systems with Singularities.

Ihor Samoilenko is Professor of Operations Research Department at Taras Shevchenko National University of Kyiv. The area of his expertise includes Random Evolutions and Dynamic Systems in Random Environment.