Brownian Motion : : An Introduction to Stochastic Processes / / René L. Schilling, Lothar Partzsch.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• VerfasserIn: Schilling, René L.,; Partzsch, Lothar,
• MitwirkendeR: Böttcher, Björn,
• TeilnehmendeR: Böttcher, Björn.
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2012]; ©2012
• Year of Publication: 2012
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (380 p.)

Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has infl...

Table of Contents

• Frontmatter
• Preface
• Contents
• Dependence chart
• Index of notation
• Chapter 1. Robert Brown’s new thing
• Chapter 2. Brownian motion as a Gaussian process
• Chapter 3. Constructions of Brownian motion
• Chapter 4. The canonical model
• Chapter 5. Brownian motion as a martingale
• Chapter 6. Brownian motion as a Markov process
• Chapter 7. Brownian motion and transition semigroups
• Chapter 8. The PDE connection
• Chapter 9. The variation of Brownian paths
• Chapter 10. Regularity of Brownian paths
• Chapter 11. The growth of Brownian paths
• Chapter 12. Strassen’s Functional Law of the Iterated Logarithm
• Chapter 13. Skorokhod representation
• Chapter 14. Stochastic integrals: L2-Theory
• Chapter 15. Stochastic integrals: beyond L2T
• Chapter 16. Itô’s formula
• Chapter 17. Applications of Itô’s formula
• Chapter 18. Stochastic differential equations
• Chapter 19. On diffusions
• Chapter 20. Simulation of Brownian motion
• Appendix
• Index