STAT 507 (Fall 2017)
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
Place:  ST 127
Lectures Schedule and Tutorials 
Lectures schedule (L01)
Tutorials  schedule (T01)
Monday/Wednesday/Friday  15:00-15:50  (ST 127)
 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, Monday, September 11, 2017 (ST 127)
  Quiz#1: 15:00, Monday, October 2, 2017 (ST 127)
Midterm:  15:00-15:50, Monday, October 30, 2017 (ST 127)
Quiz#2: 15:00, Monday, November 27, 2017 (ST 127)
Last day of class: 15:00, Friday, December 8, 2017
 
Final Exam:
Monday, December 18, 3:30-5:30pm, Room-TBA

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/stat507Fall17.html/

Midterm and Quizzes:
There will be 1 Midterm (October 30 Monday, 15:00am, ENE 328) and 2 Quizzes (Mondays, October 2 and November 27, 15:00am, ENE 328). 

Final Exam:
TBA

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 30, 2017, Monday, 15:00, ST 127
Quizzes (2)
20%=2x10%
Oct 2 & Nov 27, Monday, 15:00, ST 127
Final Exam 50%  Monday, December 18, 3:30-5:30pm, Room-TBA
Homework Assignments
Not for Credit but for your practice


Tentative Lectures Schedule for STAT 507
Month
Day
Monday
Day
Wednesday
Day
Friday
Sep
11
Lec1: Intro to Probability Theory
(Complimentary Notes: Basics in Probability)
13
Lec2: Stochastic Processes (2.9)
15
Lec3: Markov Chains (MC): Introduction (4.1)
Sep
18
Lec4: MC: Chapman-Kolmogorov Equations (4.2) 20
Lec5: MC: Classification of States (4.3): Accessible States, Classes, Irreducible MC 22
Lec6:  MC: Classification of States (4.3): Recurrent and Transient States; Random Walk
Sep
25
Lec7: MC:  Limiting Probabilities (4.4) 27
Lec8: MC: Limiting Probabilities. Example-Insurance Claim (4.4) (cont'd Lec7) 29
Lec9: MC: Some Applications (4.5)
Oct
2
Quiz#1 (based on Lectures 1-9)
4
Lec10: MC: Mean Time Spent in Transient States (4.6) 6
Lec11: Exponential distribution   (5.2.1)
Oct
9
Thanksgiving Day (No Lecture)
11
Lec12:  Poisson Process (PP): Counting Process ( 5.3.1) and Definition of PP (5.3.2) 13
Lec13: PP: Waiting Time Distribution (5.3.3)
Oct
16
Lec14: PP: Further Properties (5.3.4) 18
Lec15: PP: Conditional Distribution of Arrival Times (5.3.5) 20
Lec16:  PP: Sampling of PP (5.3.5)
Oct
23
Lec17: PP: Generalizations (5.4.1) 25
Lec18: PP: Compound PP (5.4.2) 27
Lec19: PP: Mixed PP (5.4.3)
Oct-Nov
30
MIDTERM (based on Lectures 1-18)
1
Lec20: Continuous-time Markov Chains (CTMC): Intro (6.1-6.2) 3
Lec21: CTMC: Birth& Death Processes (6.3) and Transition Probability Function (6.4)
Nov
6
Lec22: CTMC: Chapman-Kolmogorov Equations (6.4) 8
Lec23: CTMC: Limiting Probabilities (6.5)
10
November 10-13:
Reading Day (No Lecture)
Nov
13
15
 Lec24: CTMC: Computing the Transition Probabilities (6.8) 17
Lec25: Renewal Theory: Intro (7.1), Renewal Process, Properties.
Nov
20
Lec26:  Renewal Theory: Some Distributions (7.2), Renewal Equation. Limit Theorems (7.3) 22
Lec27: Brownian Motion (BM) (10.1); Variations and Martingales Properties (10.3) 24
Lec28:  BM: Pricing Stock Options and Black-Scholes Formula (10.4.1-10.4.2)
Nov-Dec
27
Quiz#2 (based on Lectures 20-28)
29
Lec29: BM: Black-Scholes Formula's Derivation 1
Lec30: BM: Black-Scholes Formula's Interpretation 
Dec
4
Lec31: Stationary Processes (10.7) 6
Lec32: Simulation Methods (11.2-11.3)
Table of Random Digits
8
Lec33: Course Review.



Announcements: 

Midterm: Monday, October 30, 15:00-15:50, ST 127
(based on Lectures 1-18; NO Aids, Basic calculator is allowed)

PERMANENT ROOM CHANGE
for Classes Starting Wednesday, September 13th:
ST 127

Please, use your @ucalgary.ca email to communicate with your instructo


 
Homework Assignments
Solutions to Chapters_2_4

TND
TEF
This page was updated on October 19, 2017.