Brownian Motion and Stochastic Calculus

Karatzas, Ioannis & Steven Shreve

ISBN 10: 0387976558 / ISBN 13: 9780387976556

Editore: Springer/Sci-Tech/Trade, 1991

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Moderate wear. Clean with no highlighting or writing detected on any pages. Cover has modest wear with minor scuffs/bends on some corners or edges. 30-day returns. Free shipping in Canada. International shipments may be subject to custom duties or other charges in accordance with the particular laws of the buyer's country but shipments to the United States should be exempt from customs since the book was published in the United States. ; Volume 113; 6.1 X 1.12 X 9.25 inches; 470 pages.

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Dati bibliografici

• Titolo: Brownian Motion and Stochastic Calculus
• Editore: Springer/Sci-Tech/Trade
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 0387976558
• ISBN 13: 9780387976556
• Rilegatura: Softcover
• Edizione: seconda edizione
• Condizione: Good+

Descrizione articolo

Riassunto

This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish 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. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization).

This 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 text is complemented by a large number of problems and exercises.

Recensione

Second Edition

I. Karatzas and S.E. Shreve

Brownian Motion and Stochastic Calculus

"A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."―MATHEMATICAL REVIEWS