Statistical Properties Of Random Process
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Introduction to Probability, Statistics, and Random Processes
The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities; limit theorems and convergence; introduction to Bayesian and classical statistics; random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion; simulation using MATLAB and R.
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.
Random Processes: Measurement, Analysis and Simulation
This book covers the basic topics associated with the measurement, analysis and simulation of random environmental processes which are encountered in practice when dealing with the dynamics, fatigue and reliability of structures in real environmental conditions. The treatment is self-contained and the authors have brought together and integrated the most important information relevant to this topic in order that the newcomer can see and study it as a whole. This approach should also be of interest to experienced engineers from fatigue laboratories who want to learn more about the possible methods of simulation, especially for use in real time on electrohydraulic computer-controlled loading machines.Problems of constructing a measuring system are dealt with in the first chapter. Here the authors discuss the choice of measuring conditions and locations, as well as the organization of a chain of devices for measuring and recording random environmental processes. Some experience gained from practical measurements is also presented. The recorded processes are further analysed by various methods. The choice is governed by the aims of the measurements and applications of the results. Chapter 2 is thus devoted to methods of random process evaluations for digital computers, both from the fatigue and dynamic point of view. The most important chapter is Chapter 3 as this presents a review of up-to-date methods of random process simulation with given statistical characteristics. These methods naturally follow those of random process analysis, and their results form initial data for the corresponding simulations algorithms, including occurrences of characteristic parameters of counting methods, reproduction of correlation theory characteristics and of autoregressive models. The simulation of non-stationary processes is treated in depth, taking into account their importance for practical applications and also the lack of information of this subject.The book is intended to help resolve many practical problems concerning the methods and quality of environmental process evaluation and simulation which can arise when up-to-date loading systems with computer control are being used in material, component and structural fatigue and dynamic research.