Fundamentals of Stochastic Filtering

This book serves as a detailed guide to non-linear stochastic filtering, combining rigorous mathematics with practical applications. Fundamentals of Stochastic Filtering is essential for those looking to deepen their understanding.

This book offers a comprehensive mathematical exploration of the non-linear stochastic filtering problem, employing contemporary methods to address complex challenges in the field. Fundamentals of Stochastic Filtering is designed for readers who possess a foundational understanding of measure theory, probability theory, and the basics of stochastic processes, making it accessible to those eager to delve into this intricate subject matter without prior knowledge of stochastic filtering itself.

Emphasizing the theoretical analysis of numerical methods, the text focuses on solutions to the filtering problem through particle methods, which are essential in modern applications. Each chapter is structured to build upon the reader's existing knowledge while introducing new concepts and techniques pertinent to the field. The book is particularly valuable for those looking to engage with recent literature, as it provides the necessary background and context for further study.

Additionally, Fundamentals of Stochastic Filtering includes appendices that state and prove most of the technical results required, ensuring that readers can grasp the foundational elements needed for a deeper understanding. Exercises and their solutions are provided throughout the book, making it a practical resource for both self-study and academic use. This combination of rigorous mathematical treatment and practical application makes the book a significant contribution to the field of stochastic filtering.