Advanced stochastic processes: Part I
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788740311150
Table of contents: title: Content; title: 1. Chapter 1. Stochastic processes: prerequisites; title: 1.1. Conditional expectation; title: 1.2. Lemma of Borel-Cantelli; title: 1.3. Stochastic processes and projective systems of measures; title: 1.4. A definition of Brownian motion; title: 1.5. Martingales and related processes; title: 2. Chapter 2. Renewal theory and Markov chains; title: 2.1. Renewal theory; title: 2.2. Some additional comments on Markov processes; title: 2.3. More on Brownian motion; title: 2.4. Gaussian vectors.; title: 2.5. Radon-Nikodym Theorem; title: 2.6. Some martingales; title: 3. Chapter 3. An introduction to stochastic processes: Brownian motion, Gaussian processes and martingales; title: 3.1. Gaussian processes; title: 3.2. Brownian motion and related processes; title: 3.3. Some results on Markov processes, on Feller semigroups and on the martingale problem; title: 3.4. Martingales, submartingales, supermartingales and semimartingales; title: 3.5. Regularity properties of stochastic processes; title: 3.6. Stochastic integrals, Itô’s formula; title: 3.7. Black-Scholes model; title: 3.8. An Ornstein-Uhlenbeck process in higher dimensions; title: 3.9. A version of Fernique’s theorem; title: 3.10. Miscellaneous