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  • Print publication year: 2017
  • Online publication date: February 2018

Preface

Summary

This book is written with the express purpose of providing the readership with a reasonably self-contained treatise on stochastic dynamical systems whilst emphasizing on a class of applications that pervade across several disciplines and thus has a general appeal. The targeted audience are doctoral students, researchers and practitioners in science and engineering who wish to understand and exploit the principles of stochastic dynamics as a tool to address their scientific or applied problems. In view of the stated aim, what one should not expect is a treatment that might be deemed rigorous enough by researchers in pure and applied mathematics. Moreover, this book deals only with diffusive stochastic processes and does not address non-Markovian and / or non-diffusive stochastic dynamical systems.

With these broad goals in mind, the question as to whether there are similar other books may naturally arise. Alternatively, one may ask if there are any aspects of originality that we, the authors, could lay our claim to. Indeed there are a number of very well-written mathematical texts on stochastic processes and calculus, some of which also cover applications to such areas as finance (e.g., stock options), biology (e.g., birth–death processes) and estimation or control. Talking of applications, there are several mathematical texts on stochastic filtering problems, even though the focus therein may not so much be on the applied aspects covering higher dimensional filtering and identification problems—an area given some prominence in this book. There are even monographs dedicated entirely to the exploitation of the theory of stochastic processes and calculus to numerical integration of stochastic differential equations. Despite such plentiful and laudatory compilations, there is, to the best of our knowledge, no book or monograph on stochastic processes that simultaneously furnishes a reasonably in-depth treatment of the problem of global optimization based on stochastic search, thereby foregrounding the role of stochastic processes and calculus in the development of robust optimization schemes. Another novel feature is the use of change of measures as the driving refrain in most of the applications covered in this book-from numerical solutions to stochastic differential equations to filtering to global optimization.