Lecturer

Prof. Boris Tsirelson, School of Mathematical Sciences.

Time and place

Monday 17-20 Kaplun 324.

Prerequisites

Both M.Sc. students and enthusiastic third-year B.Sc. students are welcome. Be acquainted with such things as:
a measure on a sigma-field; Lebesgue integral on R^d and on a measure/probability space;
the Hilbert space L₂ of square integrable functions on a measure/probability space;
the central limit theorem of probability theory; convergence of distributions;
the Poisson random process.

Grading policy

Written homework and oral exam.

Frequently asked questions

• White noise: what is it, roughly?
• Brownian motion: what is it, roughly?
• Scaling limit: what is it, roughly?
• Black noise: what is it, roughly?
• Black noise: is it a special case of a colored noise?
• What is all that good for?

Lecture notes

1. White noise as a scaling limit.
2. Poisson noise as a scaling limit.
3. Polynomials over the white noise.
4. Clashes between discrete and continuous.
5. Noises as semigroups of probability spaces.
6. Some non-smooth stochastic flows: reflection.
7. Some non-smooth stochastic flows: stickiness.
8. Stickiness as a nonclassical noise.
9. The Brownian web as a black noise.