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STAT502 Probability Theorey (II) (Spring 2019)
Instructor: Cheng Ouyang
Office Hours:
Time: Monday: 3:305pm; Friday: 2:304pm (or by appointment)
Location: SEO 502
Announcement:
Takehome final exam is due by noon on Friday,
May 10.
Extra office hours on the exam week are:
Wednesday 35pm; Friday 10:30noon.
Course Schedule:
Weeks 
Sections 
Brief Description 
01/14  01/18

6.16.3; 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 LindebergFeller CLT. 
04/01  04/05

9.8; 9.8; 9.8.

The LindebergFeller 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): 6.71(a)(d), 4, 15.
 HW 2 (due on Feb 06): 6.72, 7, 8
 HW 3 (due on Feb 15): 7.71, 23(part before "Now define..."), 39.
 HW 4 (due on Feb 22): 7.75 (a), 6, 17.
 HW 5 (due on Feb 29): 7.75 (c), 18, 41.
 HW 6 (due on Mar 8): 7.733; 8.82.
 HW 7 (due on Mar 18):8.84(a), 13.
 HW 8 (due on Apr 5):8.81, 9, 14.
 HW 9 (due on Apr 15): 8.817, 20, 31.
Relevant Course Materials:
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