Probability and Random Processes 4th Edtion By Geoffrey Grimmett, David Stirzaker ISBN 0198847599 978-0198847595

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ISBN 10: 0198847599

ISBN 13: 978-0198847595

Author: Geoffrey Grimmett, David Stirzaker

The fourth edition of this successful text provides an introduction to probability and random processes, with many practical applications. It is aimed at mathematics undergraduates and postgraduates, and has four main aims.

US BL To provide a thorough but straightforward account of basic probability theory, giving the reader a natural feel for the subject unburdened by oppressive technicalities.BE BL To discuss important random processes in depth with many examples.BE BL To cover a range of topics that are significant and interesting but less routine.BE BL To impart to the beginner some flavour of advanced work.BE UE
OP The book begins with the basic ideas common to most undergraduate courses in mathematics, statistics, and science. It ends with material usually found at graduate level, for example, Markov processes, (including Markov chain Monte Carlo), martingales, queues, diffusions, (including stochastic calculus with Itô’s formula), renewals, stationary processes (including the ergodic theorem), and option pricing in mathematical finance using the Black-Scholes formula. Further, in this new revised fourth edition, there are sections on coupling from the past, Lévy processes, self-similarity and stability, time changes, and the holding-time/jump-chain construction of continuous-time Markov chains. Finally, the number of exercises and problems has been increased by around 300 to a total of about 1300, and many of the existing exercises have been refreshed by additional parts. The solutions to these exercises and problems can be found in the companion volume, One Thousand Exercises in Probability, third edition, (OUP 2020).CP

Probability and Random Processes 4th Table of contents: 

Preface

Part 1: Fundamentals of Probability

1. Introduction to Probability

   • Basic Concepts of Probability
   • Sample Spaces and Events
   • Axioms of Probability
   • Conditional Probability and Independence
   • Bayes’ Theorem

2. Random Variables

   • Discrete Random Variables
   • Probability Mass Function (PMF)
   • Continuous Random Variables
   • Probability Density Function (PDF)
   • Cumulative Distribution Function (CDF)
   • Functions of Random Variables

3. Moments and Characteristic Functions

   • Expected Value and Variance
   • Higher Moments
   • Moment Generating Functions
   • Characteristic Functions and Their Properties

4. Special Probability Distributions

   • Binomial, Poisson, and Geometric Distributions
   • Uniform Distribution
   • Normal Distribution
   • Exponential and Gamma Distributions
   • Beta and Other Distributions

Part 2: Multivariable Probability

5. Joint Distributions

   • Joint Probability Distributions (Discrete and Continuous)
   • Marginal and Conditional Distributions
   • Covariance and Correlation
   • Transformations of Random Variables

6. Functions of Two or More Random Variables

   • Transformations of Random Variables
   • Bivariate Normal Distribution
   • Multivariate Normal Distribution
   • Order Statistics

Part 3: Random Processes

7. Introduction to Random Processes

   • Definition and Classification of Random Processes
   • Stationary Processes
   • Ergodicity and its Implications
   • Examples of Random Processes

8. Correlation and Spectral Density

   • Autocorrelation and Cross-Correlation Functions
   • Power Spectral Density
   • Spectral Representation of Random Processes
   • Wiener-Khinchin Theorem

9. Markov Chains and Processes

   • Discrete-Time Markov Chains
   • Continuous-Time Markov Processes
   • Transition Probabilities and Matrix Representation
   • Stationary Distributions
   • Applications of Markov Chains

10. Poisson Processes

    • Definition and Properties of Poisson Processes
    • The Exponential Inter-arrival Times
    • Applications of Poisson Processes
    • Compound Poisson Process

Part 4: Advanced Topics in Probability and Random Processes

11. Queuing Theory

    • Basic Queuing Models (M/M/1, M/M/c, etc.)
    • Little’s Law
    • Performance Measures: Waiting Times, System Utilization
    • Application to Communication Systems

12. Stochastic Processes and Their Applications

    • Brownian Motion and Random Walks
    • Renewal Processes
    • Applications in Finance and Engineering

13. Estimation and Hypothesis Testing

    • Point Estimation and Methods of Estimation
    • Maximum Likelihood Estimation (MLE)
    • Confidence Intervals
    • Hypothesis Testing: Likelihood Ratio Tests

Part 5: Appendix and References

14. Mathematical Tools for Probability
    • Calculus and Integration for Probability Theory
    • Special Functions and Integral Transforms
    • Matrix Algebra for Random Processes

References

Index

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Geoffrey Grimmett,David Stirzaker,Random Processes