Brownian Motion and Stochastic Calculus

Nonfiction, Science & Nature, Science, Physics, Mechanics, Mathematics, Statistics
Cover of the book Brownian Motion and Stochastic Calculus by Ioannis Karatzas, Steven Shreve, Springer New York
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Ioannis Karatzas, Steven Shreve ISBN: 9781461209492
Publisher: Springer New York Publication: March 27, 2014
Imprint: Springer Language: English
Author: Ioannis Karatzas, Steven Shreve
ISBN: 9781461209492
Publisher: Springer New York
Publication: March 27, 2014
Imprint: Springer
Language: English

A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.

More books from Springer New York

Cover of the book real time opthalmic ultrasonography by Ioannis Karatzas, Steven Shreve
Cover of the book Ultrasonography of Muscles and Tendons by Ioannis Karatzas, Steven Shreve
Cover of the book Inclusive Special Education by Ioannis Karatzas, Steven Shreve
Cover of the book Alien Skies by Ioannis Karatzas, Steven Shreve
Cover of the book HIV Treatments as Prevention (TasP) by Ioannis Karatzas, Steven Shreve
Cover of the book Handbook of Sociology of Aging by Ioannis Karatzas, Steven Shreve
Cover of the book Introduction to Space Systems by Ioannis Karatzas, Steven Shreve
Cover of the book Common Surgical Diseases by Ioannis Karatzas, Steven Shreve
Cover of the book The Internet for Nurses and Allied Health Professionals by Ioannis Karatzas, Steven Shreve
Cover of the book Modernizing Democracy by Ioannis Karatzas, Steven Shreve
Cover of the book Pediatric Injury Biomechanics by Ioannis Karatzas, Steven Shreve
Cover of the book Long-Term Consequences of Disasters by Ioannis Karatzas, Steven Shreve
Cover of the book Humor and Life Stress by Ioannis Karatzas, Steven Shreve
Cover of the book Elements of Marine Ecology by Ioannis Karatzas, Steven Shreve
Cover of the book Quantum Dot Devices by Ioannis Karatzas, Steven Shreve
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy