News (5 May)

Here are some more review exercises, found on the internet from similar courses elsewhere.
In Quiz 1 try both questions; In Quiz 2 ignore 2(c), and you've already done 2(a,b); In Quiz 3 try 1(a,b).

0. You can track our Donald Trump investment here. Recall we sold at 50.

1. End of semester arrangements are shown at the bottom of this page. No more office hours.

2. Some suggested review problems have been added on the homework page.

3. Grading policy. A number of students have asked about the grading policy, stated below at the start of the course. I will not change the stated policy, but it is interpreted somewhat flexibly, in that a student doing sufficiently well on the final exam will get a respectable grade even if they did poorly on the midterm.

STAT 150: Stochastic Processes (Spring 2011)

This is a second course in Probability, studying the mathematically basic kinds of random process, intended for majors in Statistics and related quantitative fields. The prerequisite is STAT 134 or similar upper-division course. If you did not get at least a B+ in that course then you will find this course very tough.

Instructor: David Aldous

Class Time: TuTh 12.30 - 2.00 in room 180 TAN

Note: this course does not have a discussion section or T.A.

Office Hours: Mondays 12.30 - 2.30 in 351 Evans

Text: An Introduction to Stochastic Modeling, Fourth Edition.
Authors: Mark Pinsky and Samuel Karlin (Academic Press).

Midterm: Thursday March 10

Final Exam Thursday May 12 3.00 - 6.00pm in room 180 Tan (the classroom).

Grading: 25% homework, 25% midterm, 50% final.

Style of course

The textbook tries to present the mathematics in as straightforward a manner as it can. I will follow the order of topics in the text; partly echoing the text and partly presenting other examples/variants. There are online lecture notes by Jim Pitman; also practice exams.

Homework

Weekly homeworks will be posted here, due in class each Tuesday (first homework due Tuesday February 1; no homework due March 15).

Note that the text has both Exercises (with solutions at end) and Problems: the homeworks are the "Problems". And a good way to study for exams is to try some of the "Exercises".

Rough schedule

Handwriting Rule

You can bring to the midterm and final exam anything in your own handwriting but no other written material. So you can bring your notes from class, your homework, summaries of the course material you have made - provided these are literally in your own handwriting without electronic intermediation. Do bring blue book or paper to write on; and a basic calculator.

Miscellaneous

If you email me (aldous@stat) please put "STAT 150" in subject.

I will occasionally mention in class some topic that interests me but isn't directly relevant to STAT 150; these links provide (entirely optional) material regarding such topics.

Topic each class (debriefing)

Tu 1/18: STAT 134 Review. X_ cards; blue-green taxis; lotto consortium; option on Normal; 3rd formula for variance; World series trick; geometric prob trick.
Th 1/20: Gambling on a favorable game; circular bus route; independent Exponential RVs.
Tu 1/25: Conditioning on the first step (applied to SSRW). Random sums. Conditional expectation as a RV. Geometry example (half-disc).
Th 1/27: Repeating uniforms; size-biasing; examples of not-Markov chains.
Tu 2/1: Markov chains specified by TM and initial distribution. Examples: Ehrenfest, Wright-Fisher; discrete queue. n-step transition probs. Analysis of 2-state chain. [Text, secs 3.1-3.3]
Th 2/3: Umbrella example. General equations for hitting probs and mean hitting times. [Text, sec 3.4]
Tu 2/8: Success runs, asymmetric RW. [Text, secs 3.5-3.6]
Th 2/10: Poisson immigration-death [Pitman lec. 6], cash management example [sec 3.6]
Tu 2/15: Branching processes [Text, secs 3.8-3.9]
Th 2/17: Stationary distributions. Doubly-stochastic, renewal age. [Text, sec 4.1 - 4.2]
Tu 2/22: Theorems relating long-run behavior to stationary distribution. Classification of states [Text, secs. 4.3 - 4.4]
Th 2/24: Birth-death chains; examples (geometric; umbrellas, Ehrenfest). RW on undirected graphs; examples (Knight's tour; torus).
Th 3/1: Poisson and Binomial RVs; Poisson process setup. Non-homogenous case. [Text, sec 5.1 - 5.2]
Th 3/3: Formulas for event times; conditional uniform distribution; merging and splitting PPs. [Text, sec 5.3 - 5.4]
Tu 3/8: Review
Th 3/10: Midterm
Tu 3/15: Spatial and marked Poisson processes. [Text, secs 5.5, 5.6.2]
Th 3/17: Continuous-time Markov chains. Setup. basic examples. [Text, secs 6.6. 6.1, 6.2]
SPRING BREAK
Tu 3/29: Forward equation. Simple examples. Stationary distributions and limit theorems. [Text, secs 6.1 - 6.3]
Th 3/31: Stationary distribution for birth-death chains; examples. [Text, sec 6.4]
Tu 4/5: Brownian motion -- properties and reflection principle. [Text, secs 8.1 - 8.2]
Th 4/7: Distributions associated with hitting times and zeros. [Text, sec. 8.2]
Tu 4/12: Invariance principle, 3 examples; exit probabilities for BM with drift. [Text, secs 8.1. and 8.4]
Th 4/14: geometric BM, hitting probabilities. Black-Scholes, Kelley diffusion. Brownian bridge. Text, secs 8.3 - 8.4]
Tu 4/19: General queuing systems; M/M/s. [Text, secs 9.1-9.2]
Th 4/21: M/G/1 and M/G/infty. [Text, sec 9.3]
Tu 4/26: Renewal setup, reward renewal theorem, equilibrium age and excess life distributions [Text, parts of Chapter 7]
Th 4/28; Martingales, Donald Trump and the Meaning of Life .
Tu 5/3: no meeting
Th 5/5: review session, usual time/room; I will prepare material.
Tu 5/10: review session, 1.00 - 2.30pm, room 330 Evans. I will answer questions. We can continue for as long as you have questions .....
Th 5/12, 3.00 - 6.00pm, room 180 Tan. FINAL EXAM.