White noises, black noises and other scaling limits

Spring 2002

Prof. Boris Tsirelson, School of Mathematical Sciences.
Time and place
Monday 17-20 Kaplun 324.
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 Rd 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

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.