Beichelt Applied Probability and Stochastic Processes, Second Edition

2. Auflage 2016
ISBN: 978-1-4822-5767-0
Verlag: Taylor & Francis
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 576 Seiten

Applied Probability and Stochastic Processes, Second Edition presents a self-contained introduction to elementary probability theory and stochastic processes with a special emphasis on their applications in science, engineering, finance, computer science, and operations research. It covers the theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates applications through the analysis of numerous practical examples. The author draws on his 50 years of experience in the field to give your students a better understanding of probability theory and stochastic processes and enable them to use stochastic modeling in their work.

New to the Second Edition

- Completely rewritten part on probability theory—now more than double in size

- New sections on time series analysis, random walks, branching processes, and spectral analysis of stationary stochastic processes

- Comprehensive numerical discussions of examples, which replace the more theoretically challenging sections

- Additional examples, exercises, and figures

Presenting the material in a student-friendly, application-oriented manner, this non-measure theoretic text only assumes a mathematical maturity that applied science students acquire during their undergraduate studies in mathematics. Many exercises allow students to assess their understanding of the topics. In addition, the book occasionally describes connections between probabilistic concepts and corresponding statistical approaches to facilitate comprehension. Some important proofs and challenging examples and exercises are also included for more theoretically interested readers.

Autoren/Hrsg.

Beichelt, Frank

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Bayesianische Inferenz
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung

Inhaltsverzeichnis

PROBABILITY THEORY
RANDOM EVENTS AND THEIR PROBABILITIES
RANDOM EXPERIMENTS
RANDOM EVENTS
PROBABILITY
CONDITIONAL PROBABILITY AND INDEPENDENCE OF RANDOM EVENTS

ONE-DIMENSIONAL RANDOM VARIABLES
MOTIVATION AND TERMINOLOGY
DISCRETE RANDOM VARIABLES
CONTINUOUS RANDOM VARIABLES
MIXTURES OF RANDOM VARIABLES
GENERATING FUNCTIONS

MULTIDIMENSIONAL RANDOM VARIABLES
TWO-DIMENSIONAL RANDOM VARIABLES
n-DIMENSIONAL RANDOM VARIABLES

FUNCTIONS OF RANDOM VARIABLES
FUNCTIONS OF ONE RANDOM VARIABLE
FUNCTIONS OF SEVERAL RANDOM VARIABLES
SUMS OF RANDOM VARIABLES

INEQUALITIES AND LIMIT THEOREMS
INEQUALITIES
LIMIT THEOREMS

STOCHASTIC PROCESSES
BASICS OF STOCHASTIC PROCESSES
MOTIVATION AND TERMINOLOGY
CHARACTERISTICS AND EXAMPLES
CLASSIFICATION OF STOCHASTIC PROCESSES
TIME SERIES IN DISCRETE TIME

RANDOM POINT PROCESSES
BASIC CONCEPTS
POISSON PROCESSES
RENEWAL PROCESSES

DISCRETE-TIME MARKOV CHAINS
FOUNDATIONS AND EXAMPLES
CLASSIFICATION OF STATES
LIMIT THEOREMS AND STATIONARY DISTRIBUTION
BIRTH AND DEATH PROCESSES
DISCRETE-TIME BRANCHING PROCESSES

CONTINUOUS-TIME MARKOV CHAINS
BASIC CONCEPTS AND EXAMPLES
TRANSITION PROBABILITIES AND RATES
STATIONARY STATE PROBABILITIES
SOJOURN TIMES IN PROCESS STATES
CONSTRUCTION OF MARKOV SYSTEMS
BIRTH AND DEATH PROCESSES
APPLICATIONS TO QUEUEING MODELS
SEMI-MARKOV CHAINS

MARTINGALES
DISCRETE-TIME MARTINGALES
CONTINUOUS-TIME MARTINGALES

BROWNIAN MOTION
INTRODUCTION
PROPERTIES OF THE BROWNIAN MOTION
MULTIDIMENSIONAL AND CONDITIONAL DISTRIBUTIONS
FIRST PASSAGE TIMES
TRANSFORMATIONS OF THE BROWNIAN MOTION

SPECTRAL ANALYSIS OF STATIONARY PROCESSES
FOUNDATIONS
PROCESSES WITH DISCRETE SPECTRUM
PROCESSES WITH CONTINUOUS SPECTRUM

REFERENCES

INDEX

Exercises appear at the end of each chapter.

Über Autor(innen)

Frank Beichelt is an honorary professor in the School of Statistics and Actuarial Science at the University of Witwatersrand. His research focuses on probability theory and mathematical statistics, including stochastic modeling in reliability, maintenance, and safety analysis. He is the author/coauthor of numerous papers and books, including the Chapman & Hall/CRC book Reliability and Maintenance: Networks and Systems. He holds a Dr. rer. nat. in mathematics and a Dr. sc. in engineering.