The first quarter in a yearly sequence of probability theory. Main topics are Independence, Borel-Cantelli lemmas, Weak and Strong Laws of Large Numbers, Weak Convergence, Characteristic functions, Central Limit Theorems, and elements from measure theory, integration and metric spaces.

The winter quarter (Stat310B) deals with random walks, conditional expectation, discrete time martingales, renewal theory and applications to Markov chains.

The spring quarter (Stat310C) is to concentrate on continuous time martingales, Brownian motion and introduction to stochastic calculus.

The Stat310 sequence is primarily for PhD students.

The course Math136/Stat219 , (Tu/Th 4:15-5:45, 200-002, see Fall 2007/8), rigorously covers material similar to Stat310A and Stat310B, emphasizing applications to Stochastic processes, instead of detailing the proofs of the key (hard) theorems.

** Prerequisites: ** Students should be
comfortable with probability at least at the
level of Stat116 and with real analysis at least
at the level of earning letter grade A
in Math171 (or in Math136/Stat219).
To test your skills complete
the quiz
( PDF ),
in 20min and compare with
posted solution
(
PDF ). Auditing Math205A till end of October is highly
recommended for those lacking prior exposure to measure theory.

** Text: ** download
STAT310 lecture notes

** Supplementary texts:**

- Durrett, Probability: Theory and Examples, 3rd edition (Ch. 1 -- 2)
- Williams, Probability with Martingales (Ch. 1 -- 8, 16 -- 18).
- Billingsley, Probability and Measure, 3rd edition (Ch. 1 -- 5).
- Grimmett and Stirzaker, Probability and Random Processes, 3rd edition (Ch. 1--5, 7).
- Varadhan, Probability Theory, download lecture notes (Ch. 1 -- 3.6).

** Meeting:** Hewlett 102, MW 12:50-2:05.

** TA led sections:** Hewlett 102, F 1:15-2:05 (Holger Hoefling).

** Instructor: **
Amir Dembo,
Sequoia 129, W 2:30-4:15 or e-mail
amir at math.stanford.edu

** TA1 [Final Q3] **: Holger Hoefling,
Sequoia 229, Tu 2:00-3:00, W 10:00-11:00
or e-mail
hhoeflin at stanford.edu

** TA2 [Final Q2] **: Alex Deng,
Sequoia 208, M 4:30-5:30, F 2:30-3:30
or e-mail
alexdeng at stanford.edu
(for example, for questions about the grading of HW1, HW3, HW5, HW7, HW9).

** TA3 [Final Q1] **: Hua Zhou,
Sequoia 234 (no office hours),
e-mail
hwachou at stanford.edu
(for questions about the grading of HW2, HW4, HW6, HW8, HW9).

** Grades **:
Judgement based on Final (50%) and Midterm (25%) exam marks,
and consistent Homework effort (25%).
At least 50% required for CR grade.

**
Midterm
**
(solution;
PDF)
Friday 11/2, 370-370, 3:45-5:15pm, closed material.
Syllabus: Chapter 1 and Sections 2.1-2.2 of the text.
Practice midterm
(PDF), (see
solution;
PDF).

**
Final:
** Monday 12/10, 260-113, 8:15-11:45am,
only a copy of lecture notes allowed.
Syllabus: Chapters 1-3 of lecture notes.
Practice final with solution
(PDF)

** Homeworks: ** are due Wednesday 2:05 p.m., on a weekly basis; Download
HW1--HW9
(PDF)
and see the solutions of:
HW1
(PDF) ,
HW2
(PDF) ,
HW3
(PDF) ,
HW4
(PDF) ,
HW5
(PDF) ,
HW6
(PDF) ,
HW7
(PDF) ,
HW8
(PDF)
and
HW9
(PDF)

** Syllabus ** (from posted lecture notes; with HW due dates).

9/24 M(1.1.1/1.1.2) W(1.1.3 ;---) F(+1.1.3) 10/1 M(1.2.1/1.2.2) W(1.2.3/1.3.1;HW1) F(+1.2.3) 10/8 M(1.3.2/1.3.3) W(1.3.4 ;HW2) F(+1.3.2/1.3.3) 10/15 M(1.3.5/1.4.1) W(1.4.2/2.1.1;HW3) F(+1.3.5) 10/22 M(2.1.2/2.2) W(2.2/2.3.1 ;HW4) F(1.4.3) 10/29 M(2.3.1/2.3.2) W(3.1 ;HW5) F(Review;Midterm) 11/5 M(3.2.1/3.2.2) W(3.2.3/3.3.1;HW6) F(+3.2.3) 11/12 M(3.3.1/3.3.2) W(3.3.3/3.4.1;HW7) F(+3.3.2) 11/19 M(----) W(----) F(----) 11/26 M(3.4.2) W(3.5.1/3.5.2;HW8) F(+3.5.1/3.5.2) 12/3 M(3.5.3) W(Review ;HW9) F(Q/A final)

** Approximately equivalent to: **

- Durrett: 1.1-1.8, 2.1-2.2,2.3a-c,2.4a,b,2.6, 2.9, parts of A.1,A.2,A.4,A.5,A.6,A.7;
- Williams: 1-8,16-18,A.1(except 3.14,4.8-4.12,6.9-6.11,7.4,A.1.12),A.3.1,A.5,A.9.1;
- Billingsley: 2--6,12--16,18,20,21,23,25,26,29, parts of 17,19,22,27,36;
- Grimmett and Stirzaker: 1.2,1.3,1.5,2.1-2.5,5.6-5.10,7.1-7.5,7.10 and parts of Ch. 3,4;
- Supplements: Stroock, Probability Theory : An analytic view (proof of CLT - pg. 59-64).

See also seminar for current activity in related areas.