Understanding Markov Chains Examples and Applications /

• Main Author: Privault, Nicolas (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2013.
• Series: Springer Undergraduate Mathematics Series,
• Subjects: Mathematics.; Probabilities.; Statistics.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.

This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience...

Table of Contents:

• Introduction
• 1) Probability Background
• 2) Gambling Problems
• 3) Random Walks
• 4) Discrete-Time Markov Chains
• 5) First Step Analysis
• 6) Classication of States
• 7) Long-Run Behavior of Markov Chains
• 8) Branching Processes
• 9) Continuous-Time Markov Chains
• 10) Discrete-Time Martingales
• 11) Spatial Poisson Processes
• 12) Reliability Theory
• Some Useful Identities
• Solutions to the Exercises
• References
• Index.