1st Edition
by Etienne Pardoux (Author)
"This well-written book provides a clear and accessible treatment of the theory of discrete and continuous-time Markov chains, with an emphasis towards applications. The mathematical treatment is precise and rigorous without superfluous details, and the results are immediately illustrated in illuminating examples. This book will be extremely useful to anybody teaching a course on Markov processes."
Jean-François Le Gall, Professor at Université de Paris-Orsay, France.
Markov
processes is the class of stochastic processes whose past and future
are conditionally independent, given their present state. They
constitute important models in many applied fields.
After an
introduction to the Monte Carlo method, this book describes discrete
time Markov chains, the Poisson process and continuous time Markov
chains. It also presents numerous applications including Markov Chain
Monte Carlo, Simulated Annealing, Hidden Markov Models, Annotation and
Alignment of Genomic sequences, Control and Filtering, Phylogenetic tree
reconstruction and Queuing networks. The last chapter is an
introduction to stochastic calculus and mathematical finance.
Features include:
- The Monte Carlo method, discrete time Markov chains, the Poisson process and continuous time jump Markov processes.
- An introduction to diffusion processes, mathematical finance and stochastic calculus.
- Applications
of Markov processes to various fields, ranging from mathematical
biology, to financial engineering and computer science.
- Numerous exercises and problems with solutions to most of them
