Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics, 113) - Softcover

Karatzas, Ioannis; Shreve, Steven

 
9780387976556: Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics, 113)
Softcover
ISBN 10: 0387976558 ISBN 13: 9780387976556
Verlag: Springer, 1991

Inhaltsangabe

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.

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Críticas

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

Reseña del editor

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.

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Verlag
Springer
Erscheinungsdatum
1991
Sprache
Englisch
ISBN 10 
0387976558
ISBN 13 
9780387976556
Einband
Tapa blanda
Anzahl der Seiten
498
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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Hamburg
Deutschland

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Vorgestellte Ausgabe

ISBN 10:  0387965351 ISBN 13:  9780387965352
Hardcover