Introduction to stochastic models / Marius Iosifescu, Nikolaos Limnios, Gheorghe Oprisan ; series editor, Nikolaos Limnios.

Format:

Book

Author/Creator:

Iosifescu, Marius.

Contributor:

Limnios, N. (Nikolaos)

Oprișan, Gheorghe.

Series:

Applied stochastic methods series.

Applied stochastic methods series

Standardized Title:

Modèles stochastiques. English

Language:

English

Subjects (All):

Stochastic processes.

Stochastic models.

Physical Description:

1 online resource (385 p.)

Edition:

1st edition

Place of Publication:

London : ISTE ; Hoboken, N.J. : Wiley, 2010.

Language Note:

English

System Details:

text file

Summary:

This book provides a pedagogical examination of the way in which stochastic models are encountered in applied sciences and techniques such as physics, engineering, biology and genetics, economics and social sciences. It covers Markov and semi-Markov models, as well as their particular cases: Poisson, renewal processes, branching processes, Ehrenfest models, genetic models, optimal stopping, reliability, reservoir theory, storage models, and queuing systems. Given this comprehensive treatment of the subject, students and researchers in applied sciences, as well as anyone looking for an introduc

Contents:

Cover; Introduction to Stochastic Models; Title Page; Copyright Page; Table of Contents; Preface; Chapter 1. Introduction to Stochastic Processes; 1.1. Sequences of random variables; 1.2. The notion of stochastic process; 1.3. Martingales; 1.3.1. Stopping time; 1.3.2. Discrete-time martingales; 1.3.3. Martingale convergence; 1.3.4. Square integrable martingales; 1.4. Markov chains; 1.4.1. Markov property; 1.4.2. Transition function; 1.4.3. Strong Markov property; 1.5. State classification; 1.5.1. Stationary probability; 1.6. Continuous-time Markov processes; 1.6.1. Transition function

1.6.2. Kolmogorov equations1.7. Semi-Markov processes; 1.7.1. Markov renewal processes; 1.7.2. Semi-Markov processes; Chapter 2. Simple Stochastic Models; 2.1. Urn models; 2.2. Random walks; 2.3. Brownian motion; 2.3.1. Introduction; 2.3.2. Basic properties; 2.4. Poisson processes; 2.5. Birth and death processes; Chapter 3. Elements of Markov Modeling; 3.1. Markov models: ideas, history, applications; 3.2. The discrete-time Ehrenfest model; 3.2.1. The microscopic chain; 3.2.2. The macroscopic chain; 3.2.3. Some characteristics of the Ehrenfest model

3.2.4. The discrete-time Ehrenfest model: history, generalizations, similar models3.3. Markov models in genetics; 3.3.1. Laws of heredity and mathematics; 3.3.2. Haploid models; 3.3.3. Models with two genotypes and without mutations; 3.3.4. Models with several genotypes and without mutations; 3.3.5. Models with two genotypes and mutations; 3.3.6. Models with several genotypes and mutations; 3.3.7. Models with partitioned population; 3.3.8. Genealogy models for large size populations; 3.4. Markov storage models; 3.4.1. Discrete-time models; 3.4.2. Continuous-time models

3.4.3. A generalized storage model3.5. Reliability of Markov models; 3.5.1. Introduction to reliability; 3.5.2. Some classes of survival distributions; 3.5.3. Discrete-time models; 3.5.4. Continuous-time models; Chapter 4. Renewal Models; 4.1. Fundamental concepts and examples; 4.2. Waiting times; 4.3. Modified renewal processes; 4.4. Replacement models; 4.5. Renewal reward processes; 4.6. The risk problem of an insurance company; 4.7. Counter models; 4.7.1. Type I counters; 4.7.2. Type II counters; 4.8. Alternating renewal processes; 4.9. Superposition of renewal processes

4.10. Regenerative processesChapter 5. Semi-Markov Models; 5.1. Introduction; 5.2. Markov renewal processes; 5.2.1. Definitions; 5.2.2. Markov renewal theory; 5.3. First-passage times and state classification; 5.3.1. Stationary distribution and asymptotic results; 5.4. Reliability; 5.5. Reservoir models; 5.5.1. Model I; 5.5.2. Model II; 5.6. Queues; 5.6.1. The G/M/1 queue; 5.6.2. The M/G/1 queue; 5.7. Digital communication channels; Chapter 6. Branching Models; 6.1. The Bienaymé-Galton-Watson model; 6.1.1. Historical considerations; 6.1.2. Some elementary results; 6.1.3. A fundamental example

6.1.4. Extinction probability: critical theorem

Notes:

"First published 2007 in France by Hermes Science/Lavoisier entitled: Modeles stochastiques"--t.p. verso.

Includes bibliographical references and index.

ISBN:

9781118623527

1118623525

9781118623220

1118623223

9781299315655

1299315658

9780470394076

0470394072

OCLC:

830627895