Share

Markov Processes from K. Itô's Perspective

2003-05-26 Mathematics
Download Markov Processes from K. Itô's Perspective PDF Online Free

Author :
Release : 2003-05-26
Genre : Mathematics
Kind : eBook
Book Rating : 435/5 ( reviews)

GET EBOOK


Book Synopsis Markov Processes from K. Itô's Perspective by : Daniel W. Stroock

Download or read book Markov Processes from K. Itô's Perspective written by Daniel W. Stroock. This book was released on 2003-05-26. Available in PDF, EPUB and Kindle. Book excerpt: Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes.

Markov Processes

1992 Mathematics
Download Markov Processes PDF Online Free

Author :
Release : 1992
Genre : Mathematics
Kind : eBook
Book Rating : 559/5 ( reviews)

GET EBOOK


Book Synopsis Markov Processes by : Daniel T. Gillespie

Download or read book Markov Processes written by Daniel T. Gillespie. This book was released on 1992. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Applications

2008-11-20 Mathematics
Download Markov Processes and Applications PDF Online Free

Author :
Release : 2008-11-20
Genre : Mathematics
Kind : eBook
Book Rating : 863/5 ( reviews)

GET EBOOK


Book Synopsis Markov Processes and Applications by : Etienne Pardoux

Download or read book Markov Processes and Applications written by Etienne Pardoux. This book was released on 2008-11-20. Available in PDF, EPUB and Kindle. Book excerpt: "This well-written book provides a clear and accessible treatment of the theory of discrete and continuous-time Markov chains, with an emphasis towards applications. The mathematical treatment is precise and rigorous without superfluous details, and the results are immediately illustrated in illuminating examples. This book will be extremely useful to anybody teaching a course on Markov processes." Jean-François Le Gall, Professor at Université de Paris-Orsay, France. Markov processes is the class of stochastic processes whose past and future are conditionally independent, given their present state. They constitute important models in many applied fields. After an introduction to the Monte Carlo method, this book describes discrete time Markov chains, the Poisson process and continuous time Markov chains. It also presents numerous applications including Markov Chain Monte Carlo, Simulated Annealing, Hidden Markov Models, Annotation and Alignment of Genomic sequences, Control and Filtering, Phylogenetic tree reconstruction and Queuing networks. The last chapter is an introduction to stochastic calculus and mathematical finance. Features include: The Monte Carlo method, discrete time Markov chains, the Poisson process and continuous time jump Markov processes. An introduction to diffusion processes, mathematical finance and stochastic calculus. Applications of Markov processes to various fields, ranging from mathematical biology, to financial engineering and computer science. Numerous exercises and problems with solutions to most of them

Markov Processes

2012-12-06 Mathematics
Download Markov Processes PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 318/5 ( reviews)

GET EBOOK


Book Synopsis Markov Processes by : E. B. Dynkin

Download or read book Markov Processes written by E. B. Dynkin. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Related Problems of Analysis

1982-09-23 Mathematics
Download Markov Processes and Related Problems of Analysis PDF Online Free

Author :
Release : 1982-09-23
Genre : Mathematics
Kind : eBook
Book Rating : 127/5 ( reviews)

GET EBOOK


Book Synopsis Markov Processes and Related Problems of Analysis by : Evgeniĭ Borisovich Dynkin

Download or read book Markov Processes and Related Problems of Analysis written by Evgeniĭ Borisovich Dynkin. This book was released on 1982-09-23. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics. Professor Dynkin has made many profound contributions to the subject and in this volume are collected several of his most important expository and survey articles. The content of these articles has not been covered in any monograph as yet. This account is accessible to graduate students in mathematics and operations research and will be welcomed by all those interested in stochastic processes and their applications.

You may also like...