"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
