Diffusion Processes and their Sample Paths
(Sprache: Englisch)
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...
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Produktinformationen zu „Diffusion Processes and their Sample Paths “
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.
Klappentext zu „Diffusion Processes and their Sample Paths “
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.
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.
Inhaltsverzeichnis zu „Diffusion Processes and their Sample Paths “
- The standard Brownian motion- Brownian local times
- The general 1-dimensional diffusion
- Generators
- Time changes and killing
- Local and inverse local times
- Browinian motion in several dimensions
- A general view of diffusion in several dimentions
- Bibliography
- List of notations
- Index
Autoren-Porträt von Kiyosi Ito, Henry P. McKean
Kiyosi 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.Henry 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.
Bibliographische Angaben
- Autoren: Kiyosi Ito , Henry P. McKean
- 1996, 1996, XV, 323 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3540606297
- ISBN-13: 9783540606291
- Erscheinungsdatum: 05.01.1996
Sprache:
Englisch
Rezension zu „Diffusion Processes and their Sample Paths “
"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)
Pressezitat
"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)
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