Markov processes and applications : algorithms, networks, genome and finance / Etienne Pardoux.

Format:

Book

Author/Creator:

Pardoux, E. (Etienne), 1947-

Series:

Wiley series in probability and statistics.

Wiley-Dunod series.

Wiley series in probability and statistics

Wiley-Dunod series

Language:

English

Subjects (All):

Markov processes.

Physical Description:

1 online resource (323 p.)

Edition:

1st ed.

Place of Publication:

Chichester, U.K. : Wiley/Dunod, 2008.

Language Note:

English

Summary:

""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, giv

Contents:

Markov Processes and Applications; Contents; Preface; 1 Simulations and the Monte Carlo method; 1.1 Description of the method; 1.2 Convergence theorems; 1.3 Simulation of random variables; 1.4 Variance reduction techniques; 1.5 Exercises; 2 Markov chains; 2.1 Definitions and elementary properties; 2.2 Examples; 2.2.1 Random walk in E = Zd; 2.2.2 Bienaym ́e-Galton-Watson process; 2.2.3 A discrete time queue; 2.3 Strong Markov property; 2.4 Recurrent and transient states; 2.5 The irreducible and recurrent case; 2.6 The aperiodic case; 2.7 Reversible Markov chain

2.8 Rate of convergence to equilibrium2.8.1 The reversible finite state case; 2.8.2 The general case; 2.9 Statistics of Markov chains; 2.10 Exercises; 3 Stochastic algorithms; 3.1 Markov chain Monte Carlo; 3.1.1 An application; 3.1.2 The Ising model; 3.1.3 Bayesian analysis of images; 3.1.4 Heated chains; 3.2 Simulation of the invariant probability; 3.2.1 Perfect simulation; 3.2.2 Coupling from the past; 3.3 Rate of convergence towards the invariant probability; 3.4 Simulated annealing; 3.5 Exercises; 4 Markov chains and the genome; 4.1 Reading DNA; 4.1.1 CpG islands

4.1.2 Detection of the genes in a prokaryotic genome4.2 The i.i.d. model; 4.3 The Markov model; 4.3.1 Application to CpG islands; 4.3.2 Search for genes in a prokaryotic genome; 4.3.3 Statistics of Markov chains Mk; 4.3.4 Phased Markov chains; 4.3.5 Locally homogeneous Markov chains; 4.4 Hidden Markov models; 4.4.1 Computation of the likelihood; 4.4.2 The Viterbi algorithm; 4.4.3 Parameter estimation; 4.5 Hidden semi-Markov model; 4.5.1 Limitations of the hidden Markov model; 4.5.2 What is a semi-Markov chain?; 4.5.3 The hidden semi-Markov model; 4.5.4 The semi-Markov Viterbi algorithm

4.5.5 Search for genes in a prokaryotic genome4.6 Alignment of two sequences; 4.6.1 The Needleman-Wunsch algorithm; 4.6.2 Hidden Markov model alignment algorithm; 4.6.3 A posteriori probability distribution of the alignment; 4.6.4 A posteriori probability of a given match; 4.7 A multiple alignment algorithm; 4.8 Exercises; 5 Control and filtering of Markov chains; 5.1 Deterministic optimal control; 5.2 Control of Markov chains; 5.3 Linear quadratic optimal control; 5.4 Filtering of Markov chains; 5.5 The Kalman-Bucy filter; 5.5.1 Motivation; 5.5.2 Solution of the filtering problem

5.6 Linear-quadratic control with partial observation5.7 Exercises; 6 The Poisson process; 6.1 Point processes and counting processes; 6.2 The Poisson process; 6.3 The Markov property; 6.4 Large time behaviour; 6.5 Exercises; 7 Jump Markov processes; 7.1 General facts; 7.2 Infinitesimal generator; 7.3 The strong Markov property; 7.4 Embedded Markov chain; 7.5 Recurrent and transient states; 7.6 The irreducible recurrent case; 7.7 Reversibility; 7.8 Markov models of evolution and phylogeny; 7.8.1 Models of evolution; 7.8.2 Likelihood methods in phylogeny

7.8.3 The Bayesian approach to phylogeny

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [295]-296) and index.

ISBN:

9786612342783

9780470721872

0470721871

9781282342781

1282342789

9780470721865

0470721863

OCLC:

476225894