Markov Processes, Semigroups, and Generators

Markov Processes, Semigroups, and Generators
Author: Vassili N. Kolokoltsov
Publisher: Walter de Gruyter
Total Pages: 449
Release: 2011
Genre: Mathematics
ISBN: 3110250101

This work offers a highly useful, well developed reference on Markov processes, the universal model for random processes and evolutions. The wide range of applications, in exact sciences as well as in other areas like social studies, require a volume that offers a refresher on fundamentals before conveying the Markov processes and examples for

Generators of Markov Chains

Generators of Markov Chains
Author: Adam Bobrowski
Publisher: Cambridge University Press
Total Pages: 279
Release: 2020-11-26
Genre: Mathematics
ISBN: 1108495796

A clear explanation of what an explosive Markov chain does after it passes through all available states in finite time.

The Theory of Stochastic Processes I

The Theory of Stochastic Processes I
Author: Iosif I. Gikhman
Publisher: Springer
Total Pages: 587
Release: 2015-03-30
Genre: Mathematics
ISBN: 3642619436

From the Reviews: "Gihman and Skorohod have done an excellent job of presenting the theory in its present state of rich imperfection." --D.W. Stroock, Bulletin of the American Mathematical Society, 1980

Markov Processes, Semigroups and Generators

Markov Processes, Semigroups and Generators
Author: Vassili N. Kolokoltsov
Publisher: Walter de Gruyter
Total Pages: 449
Release: 2011-03-29
Genre: Mathematics
ISBN: 311025011X

Markov processes represent a universal model for a large variety of real life random evolutions. The wide flow of new ideas, tools, methods and applications constantly pours into the ever-growing stream of research on Markov processes that rapidly spreads over new fields of natural and social sciences, creating new streamlined logical paths to its turbulent boundary. Even if a given process is not Markov, it can be often inserted into a larger Markov one (Markovianization procedure) by including the key historic parameters into the state space. This monograph gives a concise, but systematic and self-contained, exposition of the essentials of Markov processes, together with recent achievements, working from the "physical picture" - a formal pre-generator, and stressing the interplay between probabilistic (stochastic differential equations) and analytic (semigroups) tools. The book will be useful to students and researchers. Part I can be used for a one-semester course on Brownian motion, Lévy and Markov processes, or on probabilistic methods for PDE. Part II mainly contains the author's research on Markov processes. From the contents: Tools from Probability and Analysis Brownian motion Markov processes and martingales SDE, ψDE and martingale problems Processes in Euclidean spaces Processes in domains with a boundary Heat kernels for stable-like processes Continuous-time random walks and fractional dynamics Complex chains and Feynman integral

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.

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: 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

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.

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

Nonlinear Markov Processes and Kinetic Equations

Nonlinear Markov Processes and Kinetic Equations
Author: Vassili N. Kolokoltsov
Publisher: Cambridge University Press
Total Pages: 394
Release: 2010-07-15
Genre: Mathematics
ISBN: 1139489739

A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.