Finite Markov Chains and Algorithmic Applications

In this 2002 book, the author develops the necessary background in probability theory and Markov chains then discusses important computing applications.

Olle Häggström (Author)

9780521890014, Cambridge University Press

Paperback, published 30 May 2002

126 pages, 20 b/w illus.
22.8 x 15.3 x 0.8 cm, 0.2 kg

'This elegant little book is a beautiful introduction to the theory of simulation algorithms, using (discrete) Markov chains (on finite state spaces) … highly recommended to anyone interested in the theory of Markov chain simulation algorithms.' Nieuw Archief voor Wiskunde

Based on a lecture course given at Chalmers University of Technology, this 2002 book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.

1. Basics of probability theory
2. Markov chains
3. Computer simulation of Markov chains
4. Irreducible and aperiodic Markov chains
5. Stationary distributions
6. Reversible Markov chains
7. Markov chain Monte Carlo
8. Fast convergence of MCMC algorithms
9. Approximate counting
10. Propp-Wilson algorithm
11. Sandwiching
12. Propp-Wilson with read once randomness
13. Simulated annealing
14. Further reading.

Subject Areas: Mathematical theory of computation [UYA], Optimization [PBU], Calculus & mathematical analysis [PBK]