Hidden Dynamics Of Stochastic Processes
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Hidden Dynamics of Stochastic Processes
Author: Pasquale De Marco
language: en
Publisher: Pasquale De Marco
Release Date: 2025-03-09
In the realm of uncertainty and change, where randomness and unpredictability reign supreme, lies the captivating world of stochastic processes. This book embarks on an enthralling journey into the hidden dynamics that govern seemingly chaotic systems, unveiling the secrets of randomness and unlocking the mysteries of uncertainty. Unveiling the fundamental concepts of probability, we delve into the language of chance, exploring the mathematical tools that allow us to quantify uncertainty and make sense of seemingly unpredictable events. We unravel the rich tapestry of stochastic processes, from the familiar world of coin flips and dice rolls to the complex dynamics of financial markets and biological systems. With each chapter, we uncover the profound implications of stochastic processes in various fields, from engineering and finance to biology and social sciences. We witness the power of stochastic models in predicting the behavior of complex systems, optimizing decision-making under uncertainty, and simulating the intricate dynamics of real-world phenomena. Throughout our exploration, we encounter a symphony of mathematical melodies, from the elegant simplicity of Poisson processes to the intricate harmonies of stochastic differential equations. We unlock the secrets of stationarity, unravel the mysteries of ergodicity, and traverse the fascinating world of stochastic control and optimization. Join us on this intellectual adventure as we delve into the hidden dynamics of stochastic processes, unveiling the secrets of randomness and harnessing the power of uncertainty to gain a deeper understanding of the world around us. This book is an essential guide for anyone seeking to understand the intricate workings of stochastic processes. With its comprehensive coverage of fundamental concepts, diverse applications, and captivating explanations, it is a must-read for students, researchers, and practitioners across a wide range of disciplines. If you like this book, write a review!
Hidden Markov Models
Author: Robert J Elliott
language: en
Publisher: Springer Science & Business Media
Release Date: 2008-09-27
As more applications are found, interest in Hidden Markov Models continues to grow. Following comments and feedback from colleagues, students and other working with Hidden Markov Models the corrected 3rd printing of this volume contains clarifications, improvements and some new material, including results on smoothing for linear Gaussian dynamics. In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filter are derived as special cases of the authors’ general results and new expressions for a Kalman smoother are given. The Chapters on the control of Hidden Markov Chains are expanded and clarified. The revised Chapter 4 includes state estimation for discrete time Markov processes and Chapter 12 has a new section on robust control.
Statistical Analysis of Stochastic Processes in Time
Author: J. K. Lindsey
language: en
Publisher: Cambridge University Press
Release Date: 2004-08-02
This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.