understanding markov chains examples and applications

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Understanding Markov Chains

Author : Nicolas Privault
ISBN : 9789814451512
Genre : Mathematics
File Size : 75. 65 MB
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This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions.

Understanding Markov Chains

Author : Nicolas Privault
ISBN : 9814451509
Genre : Mathematics
File Size : 38. 86 MB
Format : PDF, Kindle
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This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions.

Markov Chains

Author : J. R. Norris
ISBN : 0521633966
Genre : Mathematics
File Size : 30. 62 MB
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In this rigorous account the author studies both discrete-time and continuous-time chains. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials, in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and a careful selection of exercises and examples drawn both from theory and practice. This is an ideal text for seminars on random processes or for those that are more oriented towards applications, for advanced undergraduates or graduate students with some background in basic probability theory.

Finite Markov Chains And Algorithmic Applications

Author : Olle Häggström
ISBN : 0521890012
Genre : Computers
File Size : 45. 2 MB
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In this 2002 book, the author develops the necessary background in probability theory and Markov chains then discusses important computing applications.

Markov Chains And Stochastic Stability

Author : Sean Meyn
ISBN : 9780521731829
Genre : Mathematics
File Size : 29. 31 MB
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New up-to-date edition of this influential classic on Markov chains in general state spaces. Proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background. New commentary by Sean Meyn, including updated references, reflects developments since 1996.

Understanding Probability

Author : Henk Tijms
ISBN : 9781139511070
Genre : Mathematics
File Size : 62. 12 MB
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Understanding Probability is a unique and stimulating approach to a first course in probability. The first part of the book demystifies probability and uses many wonderful probability applications from everyday life to help the reader develop a feel for probabilities. The second part, covering a wide range of topics, teaches clearly and simply the basics of probability. This fully revised third edition has been packed with even more exercises and examples and it includes new sections on Bayesian inference, Markov chain Monte-Carlo simulation, hitting probabilities in random walks and Brownian motion, and a new chapter on continuous-time Markov chains with applications. Here you will find all the material taught in an introductory probability course. The first part of the book, with its easy-going style, can be read by anybody with a reasonable background in high school mathematics. The second part of the book requires a basic course in calculus.

A First Course In Probability And Markov Chains

Author : Giuseppe Modica
ISBN : 9781118477748
Genre : Mathematics
File Size : 35. 46 MB
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Provides an introduction to basic structures of probability with a view towards applications in information technology A First Course in Probability and Markov Chains presents an introduction to the basic elements in probability and focuses on two main areas. The first part explores notions and structures in probability, including combinatorics, probability measures, probability distributions, conditional probability, inclusion-exclusion formulas, random variables, dispersion indexes, independent random variables as well as weak and strong laws of large numbers and central limit theorem. In the second part of the book, focus is given to Discrete Time Discrete Markov Chains which is addressed together with an introduction to Poisson processes and Continuous Time Discrete Markov Chains. This book also looks at making use of measure theory notations that unify all the presentation, in particular avoiding the separate treatment of continuous and discrete distributions. A First Course in Probability and Markov Chains: Presents the basic elements of probability. Explores elementary probability with combinatorics, uniform probability, the inclusion-exclusion principle, independence and convergence of random variables. Features applications of Law of Large Numbers. Introduces Bernoulli and Poisson processes as well as discrete and continuous time Markov Chains with discrete states. Includes illustrations and examples throughout, along with solutions to problems featured in this book. The authors present a unified and comprehensive overview of probability and Markov Chains aimed at educating engineers working with probability and statistics as well as advanced undergraduate students in sciences and engineering with a basic background in mathematical analysis and linear algebra.

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