Brownian Motion and Stochastic Calculus

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Mathematics - Probability
Brownian Motion and Stochastic Calculus

Brownian Motion and Stochastic Calculus

Steven E. Shreve Ioannis Karatzas

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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).

類別:

Mathematics - Probability

年:

2002

版本:

1st edition

出版商:

Springer

語言:

english

頁數:

248