Advanced stochastic processes: Part I
Publisher: Bookboon
Published: 2013
ISBN-13: 9788740311150
Table of contents: title: Chapter 1. Stochastic processes: prerequisites; title: Conditional expectation; title: Lemma of Borel-Cantelli; title: Stochastic processes and projective systems of measures; title: A definition of Brownian motion; title: Martingales and related processes; title: Chapter 2. Renewal theory and Markov chains; title: Renewal theory; title: Some additional comments on Markov processes; title: More on Brownian motion; title: Gaussian vectors.; title: Radon-Nikodym Theorem; title: Some martingales; title: Chapter 3. An introduction to stochastic processes: Brownian motion, Gaussian processes and martingales; title: Gaussian processes; title: Brownian motion and related processes; title: Some results on Markov processes, on Feller semigroups and on the martingale problem; title: Martingales, submartingales, supermartingales and semimartingales; title: Regularity properties of stochastic processes; title: Stochastic integrals, Itô’s formula; title: Black-Scholes model; title: An Ornstein-Uhlenbeck process in higher dimensions; title: A version of Fernique’s theorem; title: Miscellaneous