STAT 507 (Fall 2015)
Intro to Stochastic Processes/Applied Probability
Course Outline
Instructor:

Anatoliy Swishchuk
E-mail: aswish@ucalgary.ca
Office: MS552
Tel.: (403) 220-3274
Office Hours: MW:1:00pm-2:00pm
Marker:
Wei Hong: wei.hong@ucalgary.ca

Place:  SA124A
Lectures Schedule and Tutorials 
Lectures schedule (L01)
Tutorials  schedule (T01)
Monday/Wednesday/Friday  15:00-15:50  (SA124A)
 None

Syllabus

Markov Chains, Classification of states, irreducibility, Limit theorems,
Absorbing chains, Generating function techniques,
Renewal theory, Ordinary and alternating renewal processes, Laplace transform techniques
Poisson processes and generalizations, Continuous-time Markov chains,
Brownian motion and stationary processes, Simulation methods
.
Course Information Sheet

 Important Class Dates:
First day of class: 15:00, Wednesday, September 8, 2015
  Quiz#1: 15:00, Monday, October 5, 2015 (SA124A)
Midterm:  15:00-15:50, Monday, November 2, 2015 (SA124A)
Quiz#2: 15:00, Monday, November 30, 2015 (SA124A)
Last day of class: 15:00, Monday, December 7, 2015
 
Final Exam:
Wednesday, December 16, 2015, 3:30-5:30pm; Place-ST 147

Recommended text:
'Introduction to Probability Models' by Sheldon Ross, 10th ed., Academic Press
Additional Source: Applied Stochastic Processes by Ming Liao, CRC Press, 2014
(you may buy it in U of C Bookstore)

Course Web Page:
The current official syllabus for this course is available in the wall pockets across from MS 476 and
on the webpage at www.math.ucalgary.ca Course Listing-Undergraduate.
There is also a web page for this course which contains the course outline, tentative course schedule,  grading scheme, important class dates, etc.
Announcements made in class will be posted there (see end of this web-page). The address of this web page is: http://people.ucalgary.ca/~aswish/stat507F15.html/

Midterm and Quizzes:
There will be 1 Midterm (November 2, Monday, 15:00am, SA124A) and 2 Quizzes (Mondays, October 5 and November 30, 15:00am, SA124A).

Final Exam: Wednesday, December 16, 2015, 3:30-5:30pm; Place-ST 147
It will cover all the materials covered in this course. 

Grading scheme (Course Evaluation):

 Exam, Midterm, Quizzes and Homework Assignments
Value (% of your final mark)
Dates
Midterm
30%
Nov 2, 2015, Monday, 15:00, SA124A
Quizzes (2)
20%=2x10%
Oct 5&Nov30, Monday, 15:00, SA124A
Final Exam 50%  Wednesday, December 16, 2015, 3:30-5:30pm; Place-ST 147
Homework Assignments
Not for Credit but for your practice


Tentative Lectures Schedule for STAT 507
Month
Day
Wednesday
Day
Friday
Day
Monday
Sep
9
Lec1: Intro to Probability Theory
(Appendix: Basic in Probability)
11
Lec2: Stochastic Processes (2.9)
14
Lec3: Markov Chains (MC): Introduction (4.1)
Sep
16
Lec4: MC: Chapman-Kolmogorov Equations (4.2) 18
Lec5: MC: Classification of States (4.3): Accessible States, Classes, Irreducible MC 21
Lec6:  MC: Classification of States (4.3): Recurrent and Transient States; Random Walk
Sep
23
Lec7: MC: Limiting Probabilities (4.4) 25
Lec8: MC: Limiting Probabilities (4.4) 28
Lec9: MC: Some Applications (4.5)
Sep-Oct
30
Lec10: MC: Mean Time Spent in Transient States (4.6)
2
Lec11: Exponential distribution   (5.2.1)
5
Quiz#1
Oct
7
Lec12:  PP: Counting Process ( 5.3.1) and Definition of PP (5.3.2) 9
Lec13: PP: Waiting Time Distribution (5.3.3) 12
Thanksgiving Day (No Lecture)
Oct
14
Lec14: PP: Further Properties (5.3.4) 16
Lec15: PP: Conditional Distribution of Arrival Times (5.3.5) 19
Lec16:  PP: Sampling of PP (5.3.5)
Oct
21
Lec17: PP: Generalizations (5.4.1) 23
Lec18: PP: Compound PP (5.4.2) 26
Lec19: PP: Mixed PP (5.4.3)
Oct-Nov
28
Lec20: Continuous-time Markov Chains (CTMC): Intro (6.1-6.2) 30
Lec21: CTMC: Birth& Death Processes (6.3) and Transition Probability Function (6.4) 2
MIDTERM
Nov
4
Lec22: CTMC: Chapman-Kolmogorov Equations (6.4) 6
Lec23: CTMC: Limiting Probabilities (6.5)
9
Lec24: CTMC: Computing the Transition Probabilities (6.8)
Nov
11
Reading Day (No Lecture) 13
Reading Day (No Lecture) 16
Lec25: Renewal Theory: Intro (7.1) 
Nov
18
Lec26: Renewal Theory: Some Distributions (7.2) 20
Lec27:  Renewal Theory: Limit Theorems (7.3) 23
Lec28: Brownian Motion (BM) (10.1);
Nov
25
Lec29:  BM: Variations and Martingales Properties (10.3)
27
Lec30: BM: Pricing Stock Options and Black-Scholes Formula (10.4.1-10.4.4) 30
Quiz#2
Dec
2
Lec31: Stationary Processes (10.7) 4
Lec32: Simulation Methods (11.2-11.3)
Table of Random Digits
7
Lec33: Simulation Methods (11.4-11.5)


Announcements: 


 
Homework Assignments
(Solutions to Chapters 2-11)
TND
TEF
Laplace Table
This page was updated on December 22, 2015.