Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics, Band 113

Seitenzahl:

470

Gewicht:

690 g

Auflage:

2nd ed. pr.

Erschienen bei:

Springer, Berlin

Beschreibung

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.

Kurzbeschreibung

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. TOC:Martingales, Stopping Times, and Filtrations.- Brownian Motion.- Stochastic Integration.- Brownian Motion and Partial Differential Equations.- Stochastic Differential Equations.- Lévy's Theory of Brownian Local Time.

Inhaltsverzeichnis

From the contents: Preface§- Martingales, Stopping Times, and Filtrations§- Brownian Motion§- Stochastic Integration§- Brownian Motion and Partial Differential Equations§- Stochastic Differential Equations§- Levy's Theory of Brownian Local Time§- Bibliography§- Index

Mehr über...

Mehr über:  Stochastik, Brownscher Bewegungsprozess

Mehr von: 

Mehr von:  Ioannis Karatzas, Steven E. Shreve, Springer, Berlin