Martingale und Prozesse
May 2018 · Walter de Gruyter GmbH & Co KG
Ebook
206
Pages
Tools
info
About this ebook
This is the third volume of the series "Moderne Stochastik" (Modern Stochastics). As a follow-up to the volume "Wahrscheinlichkeit" (Probability Theory) it gives an intrdouction to dynamical aspects of probability theory using stochastic processes in discrete time. The first part of the book covers discrete martingales - their convergenc behaviour, optional sampling and stopping, uniform integrability and essential martingale inequalities. The power of martingale techniques is illustrated in the chapters on applications of martingales in classical probability and on the Burkholder-Davis-Gundy inequalities. The second half of the book treats random walks on Zd and Rd, their fluctuation behaviour, recurrence and transience. The last two chapters give a brief introduction to probabilistic potential theory and an outlook of further developments: Brownian motion and Donsker's invariance principle
Contents
Fair Play
Conditional Expectation
Martingale
Stopping and Localizing
Martingale Convergence
L2-Martingales
Uniformly Integrable Martingales
Some Classical Results of Probability
Elementary Inequalities for Martingales
The Burkholder–Davis–Gundy Inequalities
Random Walks on Zd – the first steps
Fluctuations of Simple Random Walks on Z
Recurrence and Transience of General Random Walks
Random Walks and Analysis
Donsker's Invariance Principle and Brownian Motion
This is the third volume of the series "Moderne Stochastik" (Modern Stochastics). As a follow-up to the volume "Wahrscheinlichkeit" (Probability Theory) it gives an intrdouction to dynamical aspects of probability theory using stochastic processes in discrete time. The first part of the book cove...
Discover more
About the author
René L. Schilling, Technische Universität Dresden, Germany.
René L. Schilling, Technische Universität Dresden, Germany.
Rate this ebook
Tell us what you think.
Reading information
Smartphones and tablets
Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.
Laptops and computers
You can listen to audiobooks purchased on Google Play using your computer's web browser.
eReaders and other devices
To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device. Follow the detailed Help Center instructions to transfer the files to supported eReaders.
