Includes bibliographical references (pages 118) and index.
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.
(source: Nielsen Book Data)
From Measures to Ito Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Ito 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 Ito calculus. (source: Nielsen Book Data)