Advanced stochastic processes: Part I
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788740303988
Table of contents: title: Content; title: 1. Preface; title: 2. Chapter 1. Stochastic processes: prerequisites; title: 2.1. Conditional expectation; title: 2.2. Lemma of Borel-Cantelli; title: 2.3. Stochastic processes and projective systems of measures; title: 2.4. A definition of Brownian motion; title: 2.5. Martingales and related processes; title: 3. Chapter 2. Renewal theory and Markov chains; title: 3.1. Renewal theory; title: 3.2. Some additional comments on Markov processes; title: 3.3. More on Brownian motion; title: 3.4. Gaussian vectors; title: 3.5. Radon-Nikodym Theorem; title: 3.6. Some martingales; title: 4. Chapter 3. An introduction to stochastic processes: Brownian motion...; title: 4.1. Gaussian processes; title: 4.2. Brownian motion and related processes; title: 4.3. Some results on Markov processes, on Feller semigroups and on the martingale problem; title: 4.4. Martingales, submartingales, supermartingales and semimartingales; title: 4.5. Regularity properties of stochastic processes; title: 4.6. Stochastic integrals, Itˆo’s formula; title: 4.7. Black-Scholes model; title: 4.8. A version of Fernique’s theorem; title: 4.9. Miscellaneous; title: 5. Index