Stochastic Processes with R: An Introduction (Chapman & Hall/CRC Texts in Statistical Science)

✍ Scribed by Olga Korosteleva

• Publisher: Chapman and Hall/CRC
• Year: 2022
• Tongue: English
• Leaves: 201
• Edition: 1
• Category: Library

✦ Synopsis

Stochastic Processes with R: An Introduction cuts through the heavy theory that is present in most courses on random processes and serves as practical guide to simulated trajectories and real-life applications for stochastic processes. The light yet detailed text provides a solid foundation that is an ideal companion for undergraduate statistics students looking to familiarise themselves with stochastic processes before going onto more advanced courses.

Key Features:

• Provides complete R codes for all simulations and calculations

• Substantial scientific or popular applications of each process with occasional statistical analysis.

• Helpful definitions and examples are provided for each process.

• End of chapter exercises cover theoretical applications and practice calculations.

✦ Table of Contents

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
Author
1. Stochastic Process, Discrete-time Markov Chain
1.1. Definition of Stochastic Process
1.2. Discrete-time Markov Chain
1.3. Chapman-Kolmogorov Equations
1.4. Classification of States
1.5. Limiting Probabilities
1.6. Computations in R
1.7. Simulations in R
1.8. Applications of Markov Chain
Exercises
2. Random Walk
2.1. Definition of Random Walk
2.2. Must-Know Facts About Random Walk
2.3. Simulations in R
2.4. Applications of Random Walk
Exercises
3. Poisson Process
3.1. Definition and Must-Know Facts About Poisson
3.2. Simulations in R
3.3. Applications of Poisson Process
Exercises
4. Nonhomogeneous Poisson Process
4.1. Definition of Nonhomogeneous Poisson Process
4.2. Simulations in R
4.3. Applications of Nonhomogeneous Poisson Process
Exercises
5. Compound Poisson Process
5.1. Definition of Compound Poisson Process
5.2. Simulations in R
5.3. Applications of Compound Poisson Process
Exercises
6. Conditional Poisson Process
6.1. Definition of Conditional Poisson Process
6.2. Simulations in R
6.3. Applications of Conditional Poisson Process
Exercises
7. Birth-and-Death Process
7.1. Definition of Birth-and-Death Process
7.2. Simulations in R
7.3. Applications of Birth-and-Death Process
Exercises
8. Branching Process
8.1. Definition of Branching Process
8.2. Simulations in R
8.3. Applications of Branching Process
Exercises
9. Brownian Motion
9.1. Definition of Brownian Motion
9.2. Processes Derived from Brownian Motion
9.2.1. Brownian Bridge
9.2.2. Brownian Motion with Drift and Volatility
9.2.3. Geometric Brownian Motion
9.2.4. The Ornstein-Uhlenbeck Process
9.3. Simulations in R
9.4. Applications of Brownian Motion
Exercises
Recommended Books
List of Notations
Index