MA 583 - Introduction to Stochastic Processes-Spring 2016


Instructor: Konstantinos Spiliopoulos

Office: 111 Cummington Street, Room 222
Office Hours: Tuesday and Thursday 12:30-1:30.
Email: kspiliop_at_math.bu.edu
to send me an email replace _at_ by @.

Meets:

TuTh... 09:30-11:00AM at CAS 216


T.A.: Jia Yang


Office hours: Tuesday 2:30-3:30 and Wednesday 4-5 in MCS 149 C
Tutoring hour: Wednesday 2-3 at MCS B24


Required Text: An Introduction to Stochastic Modeling, Mark Pinsky, Samuel Karlin, 4th Edition, Academic Press
Recommended Texts:

The class will be based mostly on the required text. However, we will use both of the recommended texts, especially the first one by Karlin-Taylor for certain parts of the course and for homework problems.


Course Description: Basic probabilistic problems and methods in operations research and management science. Methods of problem formulation and solution. The course will cover basic stochastic processes such as simple random walk, Markov chains, Martingales, Poisson processes, and Brownian motion.


Prerequisites: Undergraduate Prerequisites: CAS MA 581 or CAS MA 381; or consent of instructor. Graduate Prerequisites: CAS MA 581; or consent of instructor. The students are required to have a solid understanding of basic probability and calculus.



Syllabus (tentative)


I will try to follow the syllabus as closely as possible. However it may change depending on our progress. Any changes will be announced in class and posted here.




Homework assingments:
AssingmentDue DateAssignmentMaterial Covered
Homework 1 Thursday, January 28th Chapter 1: Exercises 1.2.4, 1.2.9, 1.3.5 and Problems 1.4.2(part (a) only), 1.5.2. Chapter 2. Exercises: 2.1.5, 2.3.1, Problems: 2.1.1, 2.1.7, 2.2.1 Chapter 1 (review), Chapter 2: Sections 1-3.
Homework 2 Thursday, February 4th Chapter 2: Exercises 2.3.5, 2.4.5 and Problems 2.3.3, 2.4.3, 2.4.7, 2.5.1, 2.5.3. Chapter 2: Sections 3-5.
Homework 3 Thursday, February 11th Chapter 3: Exercises 3.3.2, 3.4.3, 3.4.7 Problems 3.2.4,3.3.8, 3.4.6, 3.4.17 Chapter 3: Sections 1-4.
Homework 4 Thursday, February 18th Chapter 3. Exercises 3.5.2, 3.6.4, 3.8.1 and Problems 3.5.2,3.5.5,3.6.7, 3.6.8, 3.8.3, 3.9.3 Chapter 3: Sections 5-9.
Homework 5 Thursday, February 25th Chapter 3: Exercises 3.9.2 and Problems 3.9.6,3.9.7, Chapter 4: Exercises 4.1.3,4.1.4,4.1.10 and Problems 4.1.5, 4.1.6, 4.1.10, 4.2.3 Chapter 3: Sections 9, Chapter 4: Sections 1-2
Homework 6 Tuesday, March 1st Chapter 4: Exercises 4.3.1, 4.3.2 and Problems 4.3.2 Chapter 4: Section 3
Homework 7 Thursday, March 24th Chapter 4: Exercises 4.4.2, 4.5.1 and Problems 4.4.1,4.4.7, Chapter 5: Exercises 5.1.1, 5.1.4, 5.1.6 and Problems 5.1.6,5.1.7,5.1.10 Chapter 4: Section 4, Chapter 5: Section 1
Homework 8 Thursday, March 31st Chapter 5: Exercises 5.3.8, 5.4.5, 5.6.2 and Problems 5.2.1, 5.3.3,5.3.10, 5.4.4, 5.4.6 Chapter 5: Section 2-6
Homework 9 Thursday, April 7th Chapter 5: Problems 5.4.7, 5.6.10. Chapter 6: Exercises 6.1.3, 6.1.5 and Problems 6.1.3, 6.1.4, 6.1.5, 6.1.8 Chapter 5: Section 5-6, Chapter 6: Section 1
Homework 10 Thursday, April 14th Chapter 6: Exercises 6.3.1, 6.4.1, 6.4.5 and Problems 6.2.2, 6.3.1, 6.3.2, 6.3.3 (for this problem use the result of Exercise 3.3), 6.4.2, 6.4.5, 6.5.2 Chapter 6: Sections 2-5
Homework 11 Thursday, April 21st Chapter 6: Problems 6.6.2, Chapter 7: Exercise 7.1.4, 7.2.2, Problems 7.1.2, 7.1.3, 7.3.2, 7.3.5 Chapter 6: Section 6, Chapter 7: Sections 1-3
Homework 12 Thursday, April 29th Chapter 7: Problems 7.4.1, Chapter 8: Exercise 8.1.2, 8.1.5a), 8.4.2, 8.4.5, Problems 8.1.3, 8.2.4, 8.4.7, 8.4.9 Chapter 7: Section 4, Chapter 8: Sections 1-4


Currently the Exam schedule is as follows:
DateAssignmentMaterial Covered
Thursday March 3, 2016 09:30am-10:30am, regular class time Midterm Chapters 1-4 (material covered in class)
Tuesday 05/03/2016 9:00am-11:00am CAS 216 Final TBA


Tentative grading policy: Your grade will be based on :(a) Homework (30%), (b) midterm exam (30%) and final exam (40%). The grading policy may change depending on the progress of the class.


Exam & Homeworks:
Exams: There will be one midterm exam and one final exam. The exam material for each one of the two exams will be announced in class and posted on the webpage of the course. The final exam will be cummulative. Hence, make sure that you have learned from your mistakes of the midterm.
Homeworks: There will be several homeworks, both theoretical and more of applied flavor. The due date of each homework will be announced in class and it will usually be 7-10 days after. Needless to say, you should work on the homework on your own, unless otherwise instructed by me. The lowest homework will be dropped if you participate in class. Late homeworks will NOT be accepted.


Make-up policy: Make up exams will be given only in extreme circumstances, and only when accompanied by appropriate documentation. Any student with a valid reason to be given a make up exam must contact me prior to the exam, either by email or in person, and present documentation at the next class session attended.