Diffusion Processes and their Sample Paths (Classics in Mathematics) 1996th Edition by Kiyosi Itô (PDF)

Description

Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.

User’s Reviews

Editorial Reviews: Review “The systematic character of the exposision, which makes from the widely ramified subject matter of the extensive literature a clear, masterly arranged whole, is a particularly valuable feature of this monograph.” (Publicationes Mathematicae) From the Inside Flap Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more-dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Ito and McKean. From the Back Cover Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean. About the Author Biography of Kiyosi ItôKiyosi Itô was born on September 7, 1915, in Kuwana, Japan. After his undergraduate and doctoral studies at Tokyo University, he was associate professor at Nagoya University before joining the faculty of Kyoto University in 1952. He has remained there ever since and is now Professor Emeritus, but has also spent several years at each of Stanford, Aarhus and Cornell Universities and the University of Minnesota.Itô’s fundamental contributions to probability theory, especially the creation of stochastic differential and integral calculus and of excursion theory, form a cornerstone of this field. They have led to a profound understanding of the infinitesimal development of Markovian sample paths, and also of applied problems and phenomena associated with the planning, control and optimization of engineering and other random systems. Professor Itô has been the inspirer and teacher of an entire generation of Japanese probabilists. Biography of Henry McKeanHenry McKean was born on December 14, 1930, in Wenham, Massachusetts. He studied mathematics at Dartmouth College, Cambridge University, and Princeton University; he received his degree from the last in 1955. He has held professional positions at Kyoto University, MIT, Rockefeller University, Weizmann Institute, Balliol College, Oxford, and the Courant Institute of Mathematical Sciences (1969 to present). His main interests are probability, Hamiltonian mechanics, complex function theory, and nonlinear partial differential equations. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I purchased this book hoping to learn about diffusion processes from the ground up from the master, Professor Ito. I was hoping it would help with some the interest-rate scenario generation techniques that are used in life insurance reserving and pension plan funding work by actuaries.Instead as I started to read the book it gets into advanced calculus and advanced probability theory right off the bat. This book is targeted to math grad students and should not be read as a starting point by undergraduate students or those have been away from advanced mathematics for too long.I’m sure it is an excellent treatise on the theoretical underpinnings of these processes but would like to hear about a simpler starting point.

⭐This book contains 8 chapters starting from well summarized historical review of Brownian Motion and Diffusion processes in Preface. This book is good not only for mathematician but also for engineers since this book does not use many mathematical terminology. “Skew Brownian Motion”, which is important concept for random-walk in composite media, is shown first in this book. People who have interested in random-walk process especially in heterogeneous media should read this book.Finally, titles for each chapters are as follows.1. The standard Brownian motion, 2. Brownian local times, 3. The general 1D diffusion, 4. Generators, 5. Time changes and killing, 6. Local and inverse local times, 7. Brownian motion in several dimensions, 8.A general view of diffusion in several dimensions. Enjoy this great book !!

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