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

Instructor: Cheng Ouyang

Office Hours:

Time: Tue 11am-12pm; Wed 4-5pm
Location: SEO 502

Syllabus

Announcement:

  • Office hours have been updated!

    Course Schedule:

    Weeks Sections Brief Description
    01/13 - 01/17 6.1-6.3; 6.5; 6.6 Review of various concepts of convergence; L^p convergence; More on L^p convergence.
    01/20 - 01/24 No Class(Monday); 7.1, 7.2; 7.2 Truncation and equivalence; A general weak law of large numbers
    01/27 - 01/31 7.3; 7.3 ; 7.3 Almost Sure Convergence of Sums.
    02/03 - 02/07 7.4; 7.5; 7.6 Strong law of large numbers; SLLN for IID sequences; The Kolmogorov three series theorem
    02/10 - 02/14 7.6; 8.1; 8.2 The Kolmogorov three series theorem; Basic definitions; Scheffe's lemma.
    02/17 - 02/21 8.2; 8.3 Scheffe's Lemma; Skorohod Theorem.
    02/24 - 02/28 8.3; 8.4; 8.5. The baby Skorohod theorem; Weak Convergence equivalences, Portmanteau theorem; More relations among modes of convergence.
    03/02 - 03/06 8.7; 9.1, 9.2; 9.3. Convergence to types theorem; Momoent generating functions and central limit theorem, Characteristic functions; Expansions.
    03/09 - 03/13 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.
    03/16 - 03/27 Spring Break Spring Break
    03/30 - 04/03 9.6; 9.6; 9.7 Proof of the Continuity Theorem; Proof of the Countinuity Theorem; The Lindeberg-Feller CLT.
    04/06 - 04/10 9.8; 9.8; 9.8. The Lindeberg-Feller CLT.
    04/06 - 04/10 10.2; 10.3; 10.3 Definition of Conditional Expectation; Properties of Conditional Expectation; Properties of Conditional Expectation.
    04/13 - 04/17 10.4; 10.6; 10.7. Martingales; Connections between Martingales and Submartingales; Stopping Times.
    04/20 - 04/24 10.8; 10.8; 10.8 Positive super martingales.
    04/27 - 05/01 10.10; 10.11; 10.12 Martingale and Submartingale Convergence; Regularity and Closure; Regularity and Stopping.
    (We are currently 1 week behind the schedule.)

    Homework (updated weekly):

    • HW #1: 6.7-2, 7, 8
    • HW #2: 7.7-1, 23(part before "Now define..."), 39.
    • HW #3: 7.7-5 (a), 6, 17.
    • HW #4: 7.7-5 (c), 18, 41.
    • HW #5: 7.7-33; 8.8-2.
    • HW #6: 8.8-4(a), 13.
    • HW #7: 8.8-1, 9, 14.
    • HW #8: 8.8-17, 20, 31.
    • HW #9: 9.9-9(a) (b) (c), 16, 28
    • HW #10: 9.9-1, 4;
    • HW #11 10.17-1(a) (b) (c).
    • HW # 12 10.17-7, 13

    Relevant Course Materials:

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