MA 581 - Introduction to Stochastic Processes-Spring 2015


Instructor: Konstantinos Spiliopoulos

Office: 111 Cummington Street, Room 222
Office Hours: Monday and Wednesday 11-12.
Email: kspiliop_at_math.bu.edu
to send me an email replace _at_ by @.

Meets:

MWF... 09:00-10:00AM at CAS 314


T.A.: Matthew Morse, mrmorse@bu.edu


Office hours: Tuesday 2:00-3:00 and Thursday 11:00-12:00 at MCS 145 (111 Cummington Mall-Mathematics and Statistics department).
Tutoring hour: Thursday 1-2pm


Required Text: A course in Probability, Neil A. Weiss, Pearson
The class will be based mostly on the required text.


Course Description: Basic probability, conditional probability, independence. Discrete and continuous random variables, mean and variance, functions of random variables, moment generating function. Jointly distributed random variables, conditional distributions, independent random variables. Methods of transformations, law of large numbers, central limit theorem. Cannot be taken for credit in addition to CAS MA 381.


Prerequisites: Undergraduate Prerequisites: CAS MA 225 or CAS MA 230; or consent of instructor. Graduate Prerequisites: CAS MA 225 or CAS MA 230; or consent of instructor.



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:
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AssingmentDue DateAssignmentMaterial Covered
Homework 1 Monday, February 2nd Chapter 1. Exercises 1.4, 1.9, 1.16, 1.18, 1.31, 2.11, 2.24, 2.27, 2.44, 2.46 Chapter 1, Chapter 2: Sections 1-2.
Homework 2 Friday, February 6th Chapter 2: Exercises 2.67. Chapter 3: 3.7, 3.17, 3.26, 3.32, 3.63, 3.64 Chapter 2 and 3.
Homework 3 Wednesday, February 11th Chapter 4: 4.9, 4.11, 4.12, 4.19, 4.23, 4.31, 4.44 Chapter 4: Sections 1-3.
Homework 4 Wednesday, February 18th Chapter 4: 4.45, 4.47, 4.55, 4.68, 4.72, Chapter 5: 5.7, 5.14, 5.29 Chapter 4: Sections 3-4. Chapter 5: Sections 1-2.
Homework 5 Wednesday, February 25th Chapter 5: 5.45, 5.49, 5.62, 5.65, 5.70, 5.80, 5.84, 5.96, 5.97, 5.116 Chapter 5: Sections 3-8
Homework 6 Wednesday, March 4th Chapter 6: 6.1a)b), 6.13, 6.28, 6.46, 6.52,6.63, 6.74, 6.90, 6.103, 6.108 Chapter 6
Homework 7 Wednesday, March 18th Chapter 7: 7.5, 7.19, 7.36, 7.42, 7.47, 7.49, 7.64, 7.72, 7.98, 7.102 Chapter 7: Section 1-4
Homework 8 Wednesday, March 25th Chapter 7: 7.119, 7.120, 7.126, Chapter 8: 8.3, 8.7, 8.16, 8.21, 8.33, 8.43, 8.67, 8.72 Chapter 7: Section 5 and Chapter 8: Sections 1-4
Homework 9 Wednesday, April 1st Chapter 8: 8.94, 8.102, 8.105, 8.116, 8.120, 8.127, 8.146, 8.152 Chapter 8: Sections 5-7
Homework 10 Wednesday, April 8th Chapter 9: 9.2, 9.9, 9.21, 9.25, 9.39, 9.45, 9.64, 9.67, 9.93, 9.94, 9.118, 9.121 Chapter 9: Sections 1-6
Homework 11 Wednesday, April 15th Chapter 9: 9.148, 9.152, Chapter 10: 10.9, 10.13, 10.23, 10.29, 10.52, 10.61, 10.64, 10.78 Chapter 9: Section 7, Chapter 10: Sections 1-4
Homework 12 Monday, April 27th Chapter 10: 10.103, 10.106, Chapter 11: 11.3, 11.5, 11.25, 11.26, 11.40, 11.41 (only parts a,b), 11.43 (only parts a,b,c and only if you feel like playing with simulation do parts d,e,f), 11.55 (only part b), 11.59, 11.64 Chapter 10: Section 5, Chapter 11: Sections 1-4


Currently the Exam schedule is as follows:
DateAssignmentMaterial Covered
Wednesday FEBRUARY 25, 2015 9am-10am, regular class time Midterm 1 Chapters 1-5 (material covered in class)
Wednesday APRIL 15, 2015 9am-10am, regular class time Midterm 2 Chapters 6-10 (material covered in class)
Thursday, MAY 07, 2015 9:00am-11:00am CAS 314 Final TBA


Tentative grading policy: Your grade will be based on :(a) Homework (20%), (b) midterm 1 exam (25%), (c) midterm 2 exam (25%), and (d) final exam (30%). The grading policy may change depending on the progress of the class.


Exam & Homeworks:
Exams: There will be two midterm exams and one final exam. The exam material for each one of the 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 midterms.
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.