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Diffusions, Markov processes, and martingales

Author: L C G Rogers; D Williams
Publisher: Cambridge, U.K. ; New York : Cambridge University Press, 2000.
Series: Cambridge mathematical library.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:

This celebrated volume gives an accessible introduction to stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Together with its companion,  Read more...

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Named Person: Kiyosi Itō; Kiyosi Itō
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: L C G Rogers; D Williams
ISBN: 0521775949 9780521775946 0521775930 9780521775939
OCLC Number: 42874839
Notes: Originally published: Chichester, West Sussex, England ; New York : Wiley, ©1994.
Description: 2 volumes : illustrations ; 23 cm.
Contents: v. 1. Foundations --
v. 2. Itô calculus. Volume 1, Foundations. Chapter I, Brownian motion. Basics about Brownian motion --
Brownian motion in higher dimensions --
Gaussian processes and Lévy processes --
Chapter II, Some classical theory. Basic measure theory --
Basic probability theory --
Stochastic processes --
Discrete-parameter Martingale theory --
Continuous-parameter Supermartingales --
Probability measures on Lusin spaces --
Chapter III, Markov processes. Transition functions and resolvents --
Feller-Dynkin processes --
Additive functionals --
Approach to Ray processes : the Martin boundary --
Ray processes --
Applications --
References for volumes 1 and 2 --
Index to volumes 1 and 2. Volume 2, Itô calculus. Some frequently used notation --
Chapter IV, Introduction to Itô calculus. Some motivating remarks --
Some fundamental ideas : previsible processes, localization, etc. --
The elementary theory of finite-variation processes --
Stochastic integrals : the L² theory --
Stochastic integrals with respect to continuous Semimartingales --
Applications of Itô's formula --
Chapter V, Stochastic differential equations and diffusions. Pathwise uniqueness, strong SDEs, and flows --
Weak solutions, uniqueness in law --
Martingale problems, Markov property --
Overture to stochastic differential geometry --
One-dimensional SDEs --
One-dimensional diffusions --
Chapter VI, The general theory. Orientation --
Debut and section theorems --
Optional projections and filtering --
Characterizing previsible times --
Dual previsible projections --
The Meyer decomposition theorem --
Stochastic integration : the general case --
Itô excursion theory --
References --
Index.
Series Title: Cambridge mathematical library.
Responsibility: L.C.G. Rogers and David Williams.
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'I welcome the paperback edition version of this masterfully written text.' Paul Embrechts, JASA 'The monograph as a whole is warmly recommended to post-PhD students of probability and will be Read more...

 
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