Brownian Motion and Stochastic Calculus (Paperback)

Ioannis Karatzas

ISBN 10: 0387976558 / ISBN 13: 9780387976556

Verlag: Springer-Verlag New York Inc., New York, NY, 1991

Paperback. 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. This book is designed as a text for graduate courses in stochastic processes. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9780387976556

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.

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

Bibliografische Details

Titel: Brownian Motion and Stochastic Calculus (...
Verlag: Springer-Verlag New York Inc., New York, NY
Erscheinungsdatum: 1991
Einband: Paperback
Zustand: new
Auflage: 2. Auflage