β Scribed by Mircea Grigoriu (auth.)
No coin nor oath required. For personal study only.
This work focuses on analyzing and presenting solutions for a wide range of stochastic problems that are encountered in applied mathematics, probability, physics, engineering, finance, and economics. The approach used reduces the gap between the mathematical and engineering literature. Stochastic problems are defined by algebraic, differential or integral equations with random coefficients and/or input. However, it is the type, rather than the particular field of application, that is used to categorize these problems.
An introductory chapter outlines the types of stochastic problems under consideration in this book and illustrates some of their applications. A user friendly, systematic exposition unfolds as follows: The essentials of probability theory, random processes, stochastic integration, and Monte Carlo simulation are developed in chapters 2--5. The Monte Carlo method is used extensively to illustrate difficult theoretical concepts and solve numerically some of the stochastic problems in chapters 6--9.
Key features:
* Computational skills developed as needed to solve realistic stochastic problems
* Classical mathematical notation used, and essential theoretical facts boxed
* Numerous examples from applied sciences and engineering
* Complete proofs given; if too technical, notes clarify the idea and/or main steps
* Problems at the end of each chapter reinforce applications; hints given.
* Good bibliography at the end of every chapter
* Comprehensive index
This work is unique, self-contained, and far from a collection of facts and formulas. The analytical and numerical methods approach for solving stochastic problems may be used for self-study by a variety of researchers, and in the classroom by first year graduate students.
Front Matter....Pages i-xiii
Introduction....Pages 1-4
Probability Theory....Pages 5-101
Stochastic Processes....Pages 103-203
ItΓ΄βs Formula and Stochastic Differential Equations....Pages 205-285
Monte Carlo Simulation....Pages 287-342
Deterministic Systems and Input....Pages 343-427
Deterministic Systems and Stochastic Input....Pages 429-548
Stochastic Systems and Deterministic Input....Pages 549-672
Stochastic Systems and Input....Pages 673-756
Back Matter....Pages 757-774
Probability Theory and Stochastic Processes; Applications of Mathematics; Partial Differential Equations; Computational Mathematics and Numerical Analysis
π SIMILAR VOLUMES
This book introduces the fundamental concepts, methods, and applications of Hausdorff calculus, with a focus on its applications in fractal systems. Topics such as the Hausdorff diffusion equation, Hausdorff radial basis function, Hausdorff derivati
Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, βThis is a text with an attitude, and it is designed to reflect, wherever possible a
<p><p>Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, thos