STAT 507 (Fall 2019)
Intro to Stochastic Processes/Applied Probability
Course Outline
Instructor:

Anatoliy Swishchuk
E-mail: aswish@ucalgary.ca
Office: MS552 
Tel.: (403) 220-3274
Office Hours: M:12:00pm-2:00pm; W: 11:00-11:50am
Place: SS 113
Lectures Schedule and Tutorials 
Lectures schedule (L01)
Tutorials  schedule (T01)
Monday/Wednesday/Friday  15:00-15:50  (SS 113)
 None

Syllabus

Markov Chains, Classification of state, 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, Friday, September 6, 2019 (SS113)
  Quiz#1: 15:00, Monday, Sept 30, 2019 (SS113)
Midterm:  15:00-15:50, Monday, October 28, 2019
Quiz#2: 15:00, Monday, November 25, 2019 (SS113)
Last day of class: 15:00, Friday, December 6, 2019
  
Final Exam: Wed, Dec 18, 15:30-17:30, ENE 243

Recommended text:
'Introduction to Probability Models' by Sheldon Ross, 10th ed., Academic Press
(Additional Optional 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/stat507Fall2018.html/

Midterm and Quizzes: 
There will be 1 Midterm (October 28 Monday, 15:00am, ) and 2 Quizzes (Mondays, September 30 and November 25, 15:00am, ).  

Final Exam: Wed, Dec 18, 15:30-17:30, ENE 243
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 28, 2019, Monday, 15:00, SS 113
Quizzes (2)
20%=2x10% 
Sept 30 & Nov 25, 2019, Monday, 15:00, SS 113

Final Exam 50%  Wed, Dec 18, 15:30-17:30, ENE 243
Homework Assignments
Not for Credit but for your practice


Tentative Lectures Schedule for STAT 507 (Fall Break: November 11-17)
Month
Day
Monday
Day
Wednesday
Day
Friday
Sep
6&9
Lec1 (Friday, Sept 6)-Lec2 (Monday, Sept 9):
1) Short History of Stochastic Processes;
2) Intro to Probability Theory
(Complimentary Notes: Basics in Probability)
11
Lec2: Stochastic Processes (2.9)
13
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 20
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. Example-Insurance Claim (4.4) (cont'd Lec7) 27
Lec9: MC: Some Applications (4.5) 
Sept-Oct
30
Quiz#1 (based on Lectures 1-7)
2
Lec10: MC: Mean Time Spent in Transient States (4.6) 4
Lec11: Exponential distribution   (5.2.1)
Oct
7
Lec12:  Poisson Process (PP): Counting Process ( 5.3.1) and Definition of PP (5.3.2)
9
Lec13:  PP: Waiting Time Distribution (5.3.3)  11
Lec14: PP: Further Properties (5.3.4)
Oct
14
Thanksgiving Day (No Lecture)
16
Lec15: PP: Conditional Distribution of Arrival Times (5.3.5) 18
Lec16:  PP: Sampling of PP (5.3.5)
Oct
21
Lec17: PP: Generalizations (5.4.1) 23
Lec18: PP: Compound PP (5.4.2) 25
Lec19: PP: Mixed PP (5.4.3)
Oct-Nov
28
MIDTERM (based on Lectures 5-18)
30
Lec20: Continuous-time Markov Chains (CTMC): Intro (6.1-6.2) 1
Lec21: CTMC: Birth& Death Processes (6.3) and Transition Probability Function (6.4) 
Nov
4
Lec22: CTMC: Chapman-Kolmogorov Equations (6.4) 6
Lec23: : CTMC: Limiting Probabilities (6.5)
8
Lec24: CTMC: Computing the Transition Probabilities (6.8) 
Nov
11
Fall Break 14
 Fall Break 16
Fall Break
Nov
18
Lec25: Renewal Theory: Intro (7.1), Renewal Process, Properties. 
20
Lec26:  Renewal Theory: Some Distributions (7.2), Renewal Equation. 
Limit Theorems (Optional)(7.3)
22
Lec27: Brownian Motion (BM) (10.1);Variations and Martingales Properties (10.3) 
Nov
25
Quiz#2 (based on Lectures 20-27)
27
Lec28:  BM: Pricing Stock Options and Black-Scholes Formula (10.4.1-10.4.2) 29
Lec29: BM: Black-Scholes Formula's and Call-Put Parity's Derivations
Dec
2
Lec30: BM: Black-Scholes Formula's Interpretation 
4
Lec31: Stationary Processes (10.7) 6
Lec32: Simulation Methods (11.2-11.3) 
Table of Random Digits



Announcements: 

Final Exam
Marks (out/100)
*
Please, use your @ucalgary.ca email to communicate with your instructor 



  
Homework Assignments
(Solutions to Chapters_2_11)
Laplace Table
TableNormalDistribution

TableExponentialFunction
This page was updated on December 20, 2019.