STAT 507 (Fall 2016)
Intro to Stochastic Processes/Applied Probability
Course Outline
Instructor:

Anatoliy Swishchuk
E-mail: aswish@ucalgary.ca
Office: MS552
Tel.: (403) 220-3274
Office Hours: TR:11:00am-12:00pm
Place:  MS 217
Lectures Schedule and Tutorials 
Lectures schedule (L01)
Tutorials  schedule (T01)
Monday/Wednesday/Friday  15:00-15:50  (MS 217)
 None

Syllabus

Markov Chains, Classification of states, irreducibility, Limit theorems,
Absorbing chains, Generating function techniques,
Renewal theory, Ordinary and alternating renewal processes,
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, Monday, September 12, 2016
  Quiz#1: 15:00, Monday, October 3, 2016 (MS 217)
Midterm:  15:00-15:50, Monday, October 31 , 2016 (MS 217)
Quiz#2: 15:00, Monday, November 28, 2016 (MS 217)
Last day of class: 15:00, Friday, December 9, 2016
 
Final Exam:
Saturday, December 17, 8-10 am, ST 131

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/stat507F16.html/

Midterm and Quizzes:
There will be 1 Midterm (October 31 Monday, 15:00am, MS 217) and 2 Quizzes (Mondays, October 3 and November 28, 15:00am, MS 217). 

Final Exam:
Saturday, December 17, 8-10 am, ST 131

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%
Oct 31, 2015, Monday, 15:00, MS 217
Quizzes (2)
20%=2x10%
Oct 3 & Nov 28, Monday, 15:00, MS 217
Final Exam 50%  Saturday, December 17, 8-10am, ST 131
Homework Assignments
Not for Credit but for your practice


Tentative Lectures Schedule for STAT 507
Month
Day
Monday
Day
Wednesday
Day
Friday
Sep
12
Lec1: Intro to Probability Theory
(Appendix: Basic in Probability)
14
Lec2: Stochastic Processes (2.9)
16
Lec3: Markov Chains (MC): Introduction (4.1)
Sep
19
Lec4: MC: Chapman-Kolmogorov Equations (4.2) 21
Lec5: MC: Classification of States (4.3): Accessible States, Classes, Irreducible MC 23
Lec6:  MC: Classification of States (4.3): Recurrent and Transient States; Random Walk
Sep
26
Lec7: MC: Limiting Probabilities (4.4) 28
Lec8: MC: Limiting Probabilities. Example-Insurance Claim (4.4) (cont'd Lec7) 30
Lec9: MC: Some Applications (4.5)
Oct
3
Quiz#1 (based on Lectures 1-8)
5
Lec10: MC: Mean Time Spent in Transient States (4.6) 7
Lec11: Exponential distribution   (5.2.1)
Oct
10
Thanksgiving Day (No Lecture)
12
Lec12:  PP: Counting Process ( 5.3.1) and Definition of PP (5.3.2) 14
Lec13: PP: Waiting Time Distribution (5.3.3)
Oct
17
Lec14: PP: Further Properties (5.3.4) 19
Lec15: PP: Conditional Distribution of Arrival Times (5.3.5) 21
Lec16:  PP: Sampling of PP (5.3.5)
Oct
24
Lec17: PP: Generalizations (5.4.1) 26
Lec18: PP: Compound PP (5.4.2) 28
Lec19: PP: Mixed PP (5.4.3)
Oct-Nov
31
MIDTERM (based on Lectures 1-18)
2
Lec20: Continuous-time Markov Chains (CTMC): Intro (6.1-6.2) 4
Lec21: CTMC: Birth& Death Processes (6.3) and Transition Probability Function (6.4)
Nov
7
Lec22: CTMC: Chapman-Kolmogorov Equations (6.4) 9
Lec23: CTMC: Limiting Probabilities (6.5)
11

Reading Day (No Lecture)
Nov
14
Lec24: CTMC: Computing the Transition Probabilities (6.8) 16
Lec25: Renewal Theory: Intro (7.1), Renewal Process, Properties 

18
Lec26: Renewal Theory: Some Distributions (7.2), Renewal Equation.
Nov
21
Lec27:  Renewal Theory: Limit Theorems (7.3) 23
Lec28: Brownian Motion (BM) (10.1); Variations and Martingales Properties (10.3) 25
Lec29:  BM: Pricing Stock Options and Black-Scholes Formula (10.4.1-10.4.2)
Nov
28
Quiz#2 (based on Lectures 20-29)
30
Lec30: BM: Black-Scholes Formula's Derivation 2
Lec31: BM: Black-Scholes Formula's Interpretation 
Dec
5
Lec32: Stationary Processes (10.7) 7
Lec33: Simulation Methods (11.2-11.3)
Table of Random Digits
9
Lec34: Course Review.



Announcements: 


Marks for Stat 507

Formula Sheet and Tables for Final Exam

Office Hours before the Final Exam: T-12-2pm, TR-1:30-3pm, Friday-12-1pm



 
Homework Assignments
Solutions to Chapters 2 - 10
TND
TEF
This page was updated on December 20, 2016.