Seminar on Brownian Motion (Fall 2021)

Time: 18:40-21:00 each Thursday

Location：Qvan 9

Orgamizer：Hang Du

Introduction: Brownian motion is a fundamental object in modern probability theory. This seminar is devoted for a conprehensive understanding of Brownian motion and related topics. We hope this seminar will lay a good foundation for future study.


Reference: [MP] Peter Mörters and Yuval Peres, Brownian Motion, Cambridge University Press. Available at here.


Schedule:

  • 9, Aug. Hang Du, Introduction + existence and continuity of BM, [MP] Chap 1.

  • 14, Aug. Chenjiayue Qi, Markov property and Martingale property of BM, [MP] Chap 2.

  • 21, Aug. Weihao Guo, Dirichlet Problem, transience and recurrence of BM, [MP] Chap 3.1-3.2.

  • 28, Aug. Hua Su, Occupation measure and Green's function of BM, [MP] Chap3.3-3.4.

  • 14, Sep. Hang Du, Hausdorff dimension and the mass distribution principle, [MP] Chap 4.1-4.2.

  • 16, Sep. Zhangsong Li, Energy method and Frostman's lemma, [MP] Chap 4.3-4.4.

  • 23, Sep. Zherui Fan, Law of iterated logarithm and Dubin's embedding theorem, [MP] Chap 5.1-5.2.

  • 30, Sep. Wenhao Zhao, Azéma-Yor embedding theorem and Donsker's invariance proinciple, [MP] Chap 5.3-5.4.

  • 7, Oct. Hang Du, 2M-B theorem; Yuyang Feng, Local time of BM, [MP] Chap 5.5-6.1.

  • 14, Oct. Yuyang Feng, Lévy's theorem and the Ray-Knight theorem for local time, [MP] Chap 6.2-6.3.

  • 21, Oct. Lin Li, Stochastic integral and conformal invariance of 2D BM, [MP] Chap 7.1-7.2.

  • 28, Oct. Haoyu Liu, Tansker's formula and Feyman-Kac formula, [MP] Chap 7.3-7.4.

  • 4, Nov. Haoyu Liu, applications of Feyman-Kac formula; Hang Du, Dirichlet problem revisted, [MP] Chap 7.4-8.1.

  • 11. Nov. Hang Du, Equilibrium measure, polar sets and the intersection of BM, [MP] Chap 8.2-8.4.