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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
Announcement:
Take-home final exam is due by noon on Friday,
May 10.
Extra office hours on the exam week are:
Wednesday 3-5pm; Friday 10:30-noon.
Course Schedule:
Weeks |
Sections |
Brief Description |
01/14 - 01/18
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6.1-6.3; 6.5; 6.6
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Review of various concepts of convergence; L^p convergence; More
on L^p convergence.
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01/21 - 01/25
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No Class(Monday); 7.1, 7.2; 7.2
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Truncation and equivalence; A general weak law of large numbers
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01/28 - 02/01
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7.3; 7.3 ; 7.3
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Almost Sure Convergence of Sums.
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02/04 - 02/08
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7.4; 7.5; 7.6
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Strong law of large numbers; SLLN for IID sequences; The Kolmogorov
three series theorem
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02/11 - 02/15
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7.6; 8.1; 8.2
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The Kolmogorov three series theorem; Basic definitions; Scheffe's lemma.
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02/18 - 02/22
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8.2; 8.3
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Scheffe's Lemma; Skorohod Theorem.
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02/25 - 02/29
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8.3; 8.4; 8.5.
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The baby Skorohod theorem; Weak Convergence equivalences,
Portmanteau theorem; More relations among modes of convergence. |
03/04 - 03/08
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8.7; 9.1, 9.2; 9.3.
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Convergence to types theorem; Momoent generating functions and
central limit theorem, Characteristic functions; Expansions. |
03/11 - 03/15
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9.4, 9.5; 9.5; 9.6;
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Moments and Derivatives, Uniqueness and Continuity; Uniqueness and
Continuity; The Selection Theorem, Tightness, and Prohorov's theorem. |
03/18 - 03/22
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9.6; 9.6; 9.7
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Proof of the Continuity Theorem; Proof of the Countinuity Theorem;
The Lindeberg-Feller CLT. |
04/01 - 04/05
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9.8; 9.8; 9.8.
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The Lindeberg-Feller CLT. |
04/08 - 04/12
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10.2; 10.3; 10.3
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Definition of Conditional Expectation; Properties of Conditional
Expectation; Properties of Conditional Expectation.
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04/15 - 04/19
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10.4; 10.6; 10.7.
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Martingales; Connections between Martingales and Submartingales;
Stopping Times. |
04/22 - 04/26
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10.8; 10.8; 10.8
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Positive super martingales. |
04/29 - 05/03
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10.10; 10.11; 10.12
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Martingale and Submartingale Convergence; Regularity and Closure;
Regularity and Stopping.
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(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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