Stochastic Methods For Modeling And Predicting Complex Dynamical Systems
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Stochastic Methods for Modeling and Predicting Complex Dynamical Systems
This Second Edition is an essential guide to understanding, modeling, and predicting complex dynamical systems using new methods with stochastic tools. Expanding upon the original book, the author covers a unique combination of qualitative and quantitative modeling skills, novel efficient computational methods, rigorous mathematical theory, as well as physical intuitions and thinking. The author presents mathematical tools for understanding, modeling, and predicting complex dynamical systems using various suitable stochastic tools. The book provides practical examples and motivations when introducing these tools, merging mathematics, statistics, information theory, computational science, and data science. The author emphasizes the balance between computational efficiency and modeling accuracy while equipping readers with the skills to choose and apply stochastic tools to a wide range of disciplines. This second edition includes updated discussion of combining stochastic models with machine learning and addresses several additional topics, including importance sampling, regression, and maximum likelihood estimate. The author also introduces a new chapter on optimal control.
Stochastic Methods for Modeling and Predicting Complex Dynamical Systems
This book enables readers to understand, model, and predict complex dynamical systems using new methods with stochastic tools. The author presents a unique combination of qualitative and quantitative modeling skills, novel efficient computational methods, rigorous mathematical theory, as well as physical intuitions and thinking. An emphasis is placed on the balance between computational efficiency and modeling accuracy, providing readers with ideas to build useful models in practice. Successful modeling of complex systems requires a comprehensive use of qualitative and quantitative modeling approaches, novel efficient computational methods, physical intuitions and thinking, as well as rigorous mathematical theories. As such, mathematical tools for understanding, modeling, and predicting complex dynamical systems using various suitable stochastic tools are presented. Both theoretical and numerical approaches are included, allowing readers to choose suitable methods in different practical situations. The author provides practical examples and motivations when introducing various mathematical and stochastic tools and merges mathematics, statistics, information theory, computational science, and data science. In addition, the author discusses how to choose and apply suitable mathematical tools to several disciplines including pure and applied mathematics, physics, engineering, neural science, material science, climate and atmosphere, ocean science, and many others. Readers will not only learn detailed techniques for stochastic modeling and prediction, but will develop their intuition as well. Important topics in modeling and prediction including extreme events, high-dimensional systems, and multiscale features are discussed.
Exploring Probability and Random Processes Using MATLAB®
"Exploring Probability and Random Processes Using MATLAB®" offers a comprehensive guide to probability theory, stochastic processes, and their practical applications, focusing on intuitive understanding and MATLAB implementation. This book provides readers with a solid foundation in probability and stochastic processes while equipping them with tools and techniques for real-world scenarios. We begin with an introduction to probability theory, covering random variables, probability distributions, and statistical measures. Readers learn how to analyze and interpret uncertainty, make probabilistic predictions, and understand statistical inference principles. Moving on to stochastic processes, we explore discrete-time and continuous-time processes, Markov chains, and other key concepts. Practical examples and MATLAB code snippets illustrate essential concepts and demonstrate their implementation in MATLAB. One distinguishing feature is the emphasis on intuitive understanding and practical application. Complex mathematical concepts are explained clearly and accessibly, making the material approachable for readers with varying mathematical backgrounds. MATLAB examples provide hands-on experience and develop proficiency in using MATLAB for probability and stochastic processes analysis. Whether you're a student building a foundation in probability theory and stochastic processes, a researcher seeking practical data analysis tools, or a practitioner in engineering or finance, this book will provide the knowledge and skills needed to succeed. With a blend of theoretical insights and practical applications, "Exploring Probability and Random Processes Using MATLAB®" is an invaluable resource.