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Title Details:
Stochastic Models and Markov Chains
Authors: Zazanis, Michael
Subject: MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PROBABILITY THEORY AND STOCHASTIC PROCESSES
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PROBABILITY THEORY AND STOCHASTIC PROCESSES > STOCHASTIC PROCESSES
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PROBABILITY THEORY AND STOCHASTIC PROCESSES > MARKOV PROCESSES
Keywords:
Markov Chains
Stochastic Processes
Stochastic Models
Applied Probability
Poisson Process
Renewal Process
Description:
Abstract:
This book is an introduction to stochastic processes and stochastic models at the undergraduate level. While the emphasis is placed in developing the theory and computational techniques, a number of applications is presented in detail. Two introductory chapters, in discrete and “continuous” probability are included. The emphasis in these chapters is placed on topics and techniques that will be useful in the study of stochastic processes. We begin this study with the simple random walk and discrete time Markov chains. Following what is becoming the standard approach in the literature, a purely probabilistic approach is used in their analysis. However, a whole separate chapter is dedicated to the algebraic treatment, including the fundamental theorem of Perron and Frobenius, because we believe that the interplay between probability and linear algebra, on one hand deepens the understanding of the concepts and, on the other, prepares the student for the computational aspects of the subject. Time reversibility in Markov chains is studied both as a fundamental concept and in terms of its computational implications. The Poisson process and its properties are studied in some depth (for an undergraduate account) whereas continuous time Markov chains are treated with emphasis on the intuitive part of the theory and on applications, in order to maintain the mathematical tools needed at a modest level. The discussion of renewal theory is extensive. It includes precise statements of Blackwell’s Theorem and the Key Renewal Theorem but not its proof. Furthermore, a whole chapter is dedicated to applications of the renewal equation to Risk Theory and mathematical population models. Unfortunately, space and time limitations prevented us from discussing regenerative processes. The presentation of Brownian motion is kept at a mathematically elementary level while the chapter on martingales includes both an elementary and a mathematically more advanced part, adequate for students with the appropriate preparation.
Linguistic Editors: Triantafillidou, Sofia
Technical Editors: Papadogonas, Ioannis
Graphic Editors: Zazanis, Michael
Type: Undergraduate textbook
Creation Date: 27-03-2025
Item Details:
ISBN 978-618-228-333-2
License: Attribution – NonCommercial – NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
DOI http://doi.org/10.57713/kallipos-1082
Handle http://hdl.handle.net/11419/14736
Bibliographic Reference: Zazanis, M. (2025). Stochastic Models and Markov Chains [Undergraduate textbook]. Kallipos, Open Academic Editions. https://doi.org/10.57713/kallipos-1082
Language: Greek
Consists of:
1. Discrete Random Variables
2. Continuous Random Variables
3. Simple Random Walk
4. Discrete Time Markov Chains
5. Applications of Markov Chains in Discrete Time - Time Reversibility
6. Algebraic Techniques in Markov Chains
7. Martingales
8. Poisson Process
9. Continuous Time Markov Chains
10. Markovian Models in Queueing Theory
11. Renewal Processes
12. Applications of Renewal Theory - Risk Theory
13. Markov Decision Processes
14. Brownian Motion
Number of pages 442
Publication Origin: Kallipos, Open Academic Editions
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