Brownian Motion and Stochastic Calculus

Steven E. Shreve Ioannis Karatzas

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).

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Table of contents :
P6138303-Standard……Page 1
P6138304-Standard……Page 2
P6138305-Standard……Page 3
P6138306-Standard……Page 4
P6138316-338-Standard……Page 15
P6138339-360-Standard……Page 37
P6138361-399-Standard……Page 59
P6138400-450-Standard……Page 98
P6138451-500-Standard……Page 149
P6138501-548-Standard……Page 199
P6138549-Standard……Page 247
P6138550-Standard……Page 248