STAT 502 - Cheng Ouyang
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STAT502 Probability Theorey (II) (Spring 2019)

Instructor: Cheng Ouyang

Office Hours:

Time: Monday: 3:30-5pm; Friday: 2:30-4pm (or by appointment)
Location: SEO 502

Syllabus


Announcement:

No class on Friday, Apr 12.

Course Schedule:

Weeks Sections Brief Description
01/14 - 01/18 6.1-6.3; 6.5; 6.6 Review of various concepts of convergence; L^p convergence; More on L^p convergence.
01/21 - 01/25 No Class(Monday); 7.1, 7.2; 7.2 Truncation and equivalence; A general weak law of large numbers
01/28 - 02/01 7.3; 7.3 ; 7.3 Almost Sure Convergence of Sums.
02/04 - 02/08 7.4; 7.5; 7.6 Strong law of large numbers; SLLN for IID sequences; The Kolmogorov three series theorem
02/11 - 02/15 7.6; 8.1; 8.2 The Kolmogorov three series theorem; Basic definitions; Scheffe's lemma.
02/18 - 02/22 8.2; 8.3 Scheffe's Lemma; Skorohod Theorem.
02/25 - 02/29 8.3; 8.4; 8.5. The baby Skorohod theorem; Weak Convergence equivalences, Portmanteau theorem; More relations among modes of convergence.
03/04 - 03/08 8.7; 9.1, 9.2; 9.3. Convergence to types theorem; Momoent generating functions and central limit theorem, Characteristic functions; Expansions.
03/11 - 03/15 9.4, 9.5; 9.5; 9.6; Moments and Derivatives, Uniqueness and Continuity; Uniqueness and Continuity; The Selection Theorem, Tightness, and Prohorov's theorem.
03/18 - 03/22 9.6; 9.6; 9.7 Proof of the Continuity Theorem; Proof of the Countinuity Theorem; The Lindeberg-Feller CLT.
04/01 - 04/05 9.8; 9.8; 9.8. The Lindeberg-Feller CLT.
04/08 - 04/12 10.2; 10.3; 10.3 Definition of Conditional Expectation; Properties of Conditional Expectation; Properties of Conditional Expectation.
04/15 - 04/19 10.4; 10.6; 10.7. Martingales; Connections between Martingales and Submartingales; Stopping Times.
04/22 - 04/26 10.8; 10.8; 10.8 Positive super martingales.
04/29 - 05/03 10.10; 10.11; 10.12 Martingale and Submartingale Convergence; Regularity and Closure; Regularity and Stopping.
(We are currently 1.5 weeks ahead of the schedule.)

Homework (updated weekly):

  • HW 1 (due on Jan 30): 6.7-1(a)(d), 4, 15.
  • HW 2 (due on Feb 06): 6.7-2, 7, 8
  • HW 3 (due on Feb 15): 7.7-1, 23(part before "Now define..."), 39.
  • HW 4 (due on Feb 22): 7.7-5 (a), 6, 17.
  • HW 5 (due on Feb 29): 7.7-5 (c), 18, 41.
  • HW 6 (due on Mar 8): 7.7-33; 8.8-2.
  • HW 7 (due on Mar 18):8.8-4(a), 13.
  • HW 8 (due on Apr 5):8.8-1, 9, 14.
  • HW 9 (due on Apr 15): 8.8-17, 20, 31.

Relevant Course Materials:


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