EAN: 9780387976556

BROWNIAN MOTION AND STOCHASTIC CALCULUS - IOANN...

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.

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