Probability Theory and Stochastic Processes
Title | Probability Theory and Stochastic Processes PDF eBook |
Author | Pierre Brémaud |
Publisher | Springer Nature |
Total Pages | 713 |
Release | 2020-04-07 |
Genre | Mathematics |
ISBN | 3030401839 |
The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive to the applications-oriented student. One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.
Probability and Stochastic Processes
Title | Probability and Stochastic Processes PDF eBook |
Author | Ionut Florescu |
Publisher | John Wiley & Sons |
Total Pages | 578 |
Release | 2014-10-27 |
Genre | Mathematics |
ISBN | 0470624558 |
A comprehensive and accessible presentation of probability and stochastic processes with emphasis on key theoretical concepts and real-world applications With a sophisticated approach, Probability and Stochastic Processes successfully balances theory and applications in a pedagogical and accessible format. The book’s primary focus is on key theoretical notions in probability to provide a foundation for understanding concepts and examples related to stochastic processes. Organized into two main sections, the book begins by developing probability theory with topical coverage on probability measure; random variables; integration theory; product spaces, conditional distribution, and conditional expectations; and limit theorems. The second part explores stochastic processes and related concepts including the Poisson process, renewal processes, Markov chains, semi-Markov processes, martingales, and Brownian motion. Featuring a logical combination of traditional and complex theories as well as practices, Probability and Stochastic Processes also includes: Multiple examples from disciplines such as business, mathematical finance, and engineering Chapter-by-chapter exercises and examples to allow readers to test their comprehension of the presented material A rigorous treatment of all probability and stochastic processes concepts An appropriate textbook for probability and stochastic processes courses at the upper-undergraduate and graduate level in mathematics, business, and electrical engineering, Probability and Stochastic Processes is also an ideal reference for researchers and practitioners in the fields of mathematics, engineering, and finance.
An Introduction to Probability and Stochastic Processes
Title | An Introduction to Probability and Stochastic Processes PDF eBook |
Author | James L. Melsa |
Publisher | Courier Corporation |
Total Pages | 420 |
Release | 2013-01-01 |
Genre | Mathematics |
ISBN | 0486490998 |
Detailed coverage of probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.
Elementary Probability Theory with Stochastic Processes
Title | Elementary Probability Theory with Stochastic Processes PDF eBook |
Author | K. L. Chung |
Publisher | Springer Science & Business Media |
Total Pages | 332 |
Release | 2013-03-09 |
Genre | Mathematics |
ISBN | 1475739737 |
This book provides an elementary introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, amply motivated, explained and illustrated with a large number of carefully selected samples. The fourth edition adds material related to mathematical finance, as well as expansions on stable laws and martingales.
Probability Theory and Stochastic Processes with Applications (Second Edition)
Title | Probability Theory and Stochastic Processes with Applications (Second Edition) PDF eBook |
Author | Oliver Knill |
Publisher | World Scientific Publishing Company |
Total Pages | 500 |
Release | 2017-01-31 |
Genre | Mathematics |
ISBN | 9789813109490 |
This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.
Introduction to Stochastic Processes
Title | Introduction to Stochastic Processes PDF eBook |
Author | Paul G. Hoel |
Publisher | Waveland Press |
Total Pages | 212 |
Release | 1986-12-01 |
Genre | Mathematics |
ISBN | 1478608994 |
An excellent introduction for computer scientists and electrical and electronics engineers who would like to have a good, basic understanding of stochastic processes! This clearly written book responds to the increasing interest in the study of systems that vary in time in a random manner. It presents an introductory account of some of the important topics in the theory of the mathematical models of such systems. The selected topics are conceptually interesting and have fruitful application in various branches of science and technology.
Introduction to Probability Theory and Stochastic Processes
Title | Introduction to Probability Theory and Stochastic Processes PDF eBook |
Author | John Chiasson |
Publisher | John Wiley & Sons |
Total Pages | 0 |
Release | 2013-04-08 |
Genre | Mathematics |
ISBN | 111838279X |
A unique approach to stochastic processes that connects the mathematical formulation of random processes to their use in applications This book presents an innovative approach to teaching probability theory and stochastic processes based on the binary expansion of the unit interval. Departing from standard pedagogy, it uses the binary expansion of the unit interval to explicitly construct an infinite sequence of independent random variables (of any given distribution) on a single probability space. This construction then provides the framework to understand the mathematical formulation of probability theory for its use in applications. Features include: The theory is presented first for countable sample spaces (Chapters 1-3) and then for uncountable sample spaces (Chapters 4-18) Coverage of the explicit construction of i.i.d. random variables on a single probability space to explain why it is the distribution function rather than the functional form of random variables that matters when it comes to modeling random phenomena Explicit construction of continuous random variables to facilitate the "digestion" of random variables, i.e., how they are used in contrast to how they are defined Explicit construction of continuous random variables to facilitate the two views of expectation: as integration over the underlying probability space (abstract view) or as integration using the density function (usual view) A discussion of the connections between Bernoulli, geometric, and Poisson processes Incorporation of the Johnson-Nyquist noise model and an explanation of why (and when) it is valid to use a delta function to model its autocovariance Comprehensive, astute, and practical, Introduction to Probability Theory and Stochastic Processes is a clear presentation of essential topics for those studying communications, control, machine learning, digital signal processing, computer networks, pattern recognition, image processing, and coding theory.