From Measures to It

From Measures to Itô Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Itô integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure theory. This text is ideal preparation for graduate-level courses in mathematical finance and perfect for any reader seeking a basic understanding of the mathematics underpinning the various applications of Itô calculus.

Spis treści:
Preface
1. Probability and measure
2. Measures and distribution functions
3. Measurable functions/random variables
4. Integration and expectation
5. Lp-spaces and conditional expectation
6. Discrete-time martingales
7. Brownian motion
8. Stochastic integrals
Bibliography
Index.