An Introduction to Markov Processes

An Introduction to Markov Processes
Author: Daniel W. Stroock
Publisher: Springer Science & Business Media
Total Pages: 213
Release: 2013-10-28
Genre: Mathematics
ISBN: 3642405231

This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineering, economics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes. Applications are dispersed throughout the book. In addition, a whole chapter is devoted to reversible processes and the use of their associated Dirichlet forms to estimate the rate of convergence to equilibrium. These results are then applied to the analysis of the Metropolis (a.k.a simulated annealing) algorithm. The corrected and enlarged 2nd edition contains a new chapter in which the author develops computational methods for Markov chains on a finite state space. Most intriguing is the section with a new technique for computing stationary measures, which is applied to derivations of Wilson's algorithm and Kirchoff's formula for spanning trees in a connected graph.

Markov Processes

Markov Processes
Author: Daniel T. Gillespie
Publisher: Gulf Professional Publishing
Total Pages: 600
Release: 1992
Genre: Mathematics
ISBN: 9780122839559

Markov process theory provides a mathematical framework for analyzing the elements of randomness that are involved in most real-world dynamical processes. This introductory text, which requires an understanding of ordinary calculus, develops the concepts and results of random variable theory.

Markov Processes for Stochastic Modeling

Markov Processes for Stochastic Modeling
Author: Oliver Ibe
Publisher: Newnes
Total Pages: 515
Release: 2013-05-22
Genre: Mathematics
ISBN: 0124078397

Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects. Therefore, this is an applications-oriented book that also includes enough theory to provide a solid ground in the subject for the reader. - Presents both the theory and applications of the different aspects of Markov processes - Includes numerous solved examples as well as detailed diagrams that make it easier to understand the principle being presented - Discusses different applications of hidden Markov models, such as DNA sequence analysis and speech analysis.

Markov Processes, Brownian Motion, and Time Symmetry

Markov Processes, Brownian Motion, and Time Symmetry
Author: Kai Lai Chung
Publisher: Springer Science & Business Media
Total Pages: 443
Release: 2005-07-15
Genre: Mathematics
ISBN: 0387220267

From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zürich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews) This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text.

Continuous Time Markov Processes

Continuous Time Markov Processes
Author: Thomas Milton Liggett
Publisher: American Mathematical Soc.
Total Pages: 290
Release: 2010
Genre: Mathematics
ISBN: 0821849492

Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, and applies this theory to various special examples.

Markov Processes

Markov Processes
Author: Evgenij Borisovic Dynkin
Publisher: Springer
Total Pages: 366
Release: 2012-08-01
Genre: Mathematics
ISBN: 9783662000335

The modem theory of Markov processes has its origins in the studies of A. A. MARKOV (1906-1907) on sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian motion (L. BACHELlER 1900, A. EIN STEIN 1905). The first correct mathematical construction of a Markov process with continuous trajectories was given by N. WIENER in 1923. (This process is often called the Wiener process.) The general theory of Markov processes was developed in the 1930's and 1940's by A. N. KOL MOGOROV, W. FELLER, W. DOEBLlN, P. LEVY, J. L. DOOB, and others. During the past ten years the theory of Markov processes has entered a new period of intensive development. The methods of the theory of semigroups of linear operators made possible further progress in the classification of Markov processes by their infinitesimal characteristics. The broad classes of Markov processes with continuous trajectories be came the main object of study. The connections between Markov pro cesses and classical analysis were further developed. It has become possible not only to apply the results and methods of analysis to the problems of probability theory, but also to investigate analytic problems using probabilistic methods. Remarkable new connections between Markov processes and potential theory were revealed. The foundations of the theory were reviewed critically: the new concept of strong Markov process acquired for the whole theory of Markov processes great importance.

Markov Processes

Markov Processes
Author: James R. Kirkwood
Publisher: CRC Press
Total Pages: 336
Release: 2015-02-09
Genre: Business & Economics
ISBN: 1482240742

Clear, rigorous, and intuitive, Markov Processes provides a bridge from an undergraduate probability course to a course in stochastic processes and also as a reference for those that want to see detailed proofs of the theorems of Markov processes. It contains copious computational examples that motivate and illustrate the theorems. The text is desi

Labelled Markov Processes

Labelled Markov Processes
Author: Prakash Panangaden
Publisher: Imperial College Press
Total Pages: 212
Release: 2009
Genre: Mathematics
ISBN: 1848162898

Labelled Markov processes are probabilistic versions of labelled transition systems with continuous state spaces. The book covers basic probability and measure theory on continuous state spaces and then develops the theory of LMPs.

Excursions of Markov Processes

Excursions of Markov Processes
Author: Robert M. Blumenthal
Publisher: Springer Science & Business Media
Total Pages: 287
Release: 2012-12-06
Genre: Mathematics
ISBN: 1468494120

Let {Xti t ~ O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the "excursions away from 0," that is pieces of path X. : T ::5 s ::5 t, with Xr- = X = 0, but X. 1= 0 for T

Markov Processes

Markov Processes
Author: Stewart N. Ethier
Publisher: John Wiley & Sons
Total Pages: 528
Release: 2009-09-25
Genre: Mathematics
ISBN: 0470317329

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "[A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference." -American Scientist "There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings." -Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts "Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference work and as a graduate textbook." -Journal of Statistical Physics Markov Processes presents several different approaches to proving weak approximation theorems for Markov processes, emphasizing the interplay of methods of characterization and approximation. Martingale problems for general Markov processes are systematically developed for the first time in book form. Useful to the professional as a reference and suitable for the graduate student as a text, this volume features a table of the interdependencies among the theorems, an extensive bibliography, and end-of-chapter problems.