## TAU:0365-4132 |
## Brownian motion | ## 2007/2008, sem. 2 |

- Lecturer
- Prof. Boris Tsirelson (School of Mathematical Sciences).
- Time and place
- Thursday 17-20 Schreiber 209.
- Prerequisites
- Be acquainted with such things as the Hilbert space
*L*_{2}of square integrable functions on a measure space. Some maturity in analysis is needed. If you did not take "Advanced probability", be ready to accept some theorems without proofs. - Grading policy
- Written homework and oral exam.

- Independent increments.

PDF or Postscript. - Markov and strong Markov.

PDF or Postscript.

Corrections: PDF or Postscript. - Random walks and Brownian motion.

PDF or Postscript. - Brownian martingales.

PDF or Postscript. - Localization.

PDF or Postscript. - Time change.

PDF or Postscript.

- Durrett R. (Richard), "Probability: theory and examples" (second edition, 1996), Chapter 7.
- Durrett R. (Richard), "Brownian motion and martingales in analysis" (1984), Chapters 1-5.

"Brownian motion is a process of tremendous practical and theoretical significance. [...] Brownian motion is a Gaussian Markov process with stationary independent increments. It lies in the intersection of three important classes of processes and is a fundamental example in each theory."

Richard DURRETT [1, p. 374].