TY  - BOOK
AU  - Ioannis Karatzas
TI  - Brownian motion and stochastic calculus
T2  -  Graduate Texts in Mathematics
SN  - 9780387976556
AV  - QA274.75 
PY  - 1998///]
CY  - USA
PB  - Springer
KW  - Mathematics
N1  - 1. Martingales, Stopping Times, and Filtrations
2. Brownian Motion
3. Stochastic Integration
4. Brownian Motion and Partial Differential Equations
5. Stochastic Differential Equations
6. P. Lévy’s Theory of Brownian Local Time
N2  - 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). ---summary provided by publisher
UR  - https://link.springer.com/book/10.1007/978-1-4612-0949-2
ER  -