STAT 507 (Fall 2018)
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:  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 7, 2018 (SS 113)
  Quiz#1: 15:00, Monday, October 1, 2018 (SS 113)
Midterm:  15:00-15:50, Monday, October 29, 2018 (SS 113
Quiz#2: 15:00, Monday, November 26, 2018 (SS 113)
Last day of class: 15:00, Friday, December 7, 2018
  
Final Exam: Tuesday, December 11, 7pm-9pm (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/stat507Fall2018.html/

Midterm and Quizzes: 
There will be 1 Midterm (October 29 Monday, 15:00am, SS 113) and 2 Quizzes (Mondays, October 1 and November 26, 15:00am, SS 113).  

Final Exam: Tuesday, December 11, 7pm-9pm, KN DANCE (KNA 163)
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 29, 2018, Monday, 15:00, SS 113
Quizzes (2)
20%=2x10% 
Oct 1 & Nov 26, 2018, Monday, 15:00, SS 113
Final Exam 50%  Tuesday, Decmber 11, 7pm-9pm, KN DANCE (KNA 163)
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
7&10
Lec1 (Friday, Sept 7)-Lec2 (Monday, Sept 10): Intro to Probability Theory
(Complimentary Notes: Basics in Probability)
12
Lec2: Stochastic Processes (2.9)
14
Lec3: Markov Chains (MC): Introduction (4.1)
Sep
17
Lec4: MC: Chapman-Kolmogorov Equations (4.2) 19
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
24
Lec7: MC:  Limiting Probabilities (4.4) 26
Lec8: MC: Limiting Probabilities. Example-Insurance Claim (4.4) (cont'd Lec7) 28
Lec9: MC: Some Applications (4.5) 
Oct
1
Quiz#1 (based on Lectures 1-9)
3
Lec10: MC: Mean Time Spent in Transient States (4.6) 5
Lec11: Exponential distribution   (5.2.1)
Oct
8
Thanksgiving Day (No Lecture)
10
Lec12:  Poisson Process (PP): Counting Process ( 5.3.1) and Definition of PP (5.3.2)  12
Lec13: PP: Waiting Time Distribution (5.3.3) 
Oct
15
Lec14: PP: Further Properties (5.3.4)  17
Lec15: PP: Conditional Distribution of Arrival Times (5.3.5) 19
Lec16:  PP: Sampling of PP (5.3.5)
Oct
22
Lec17: PP: Generalizations (5.4.1) 24
Lec18: PP: Compound PP (5.4.2) 26
Lec19: PP: Mixed PP (5.4.3)
Oct-Nov
29
MIDTERM (based on Lectures 1-18)
31
Lec20: Continuous-time Markov Chains (CTMC): Intro (6.1-6.2) 2
Lec21: CTMC: Birth& Death Processes (6.3) and Transition Probability Function (6.4) 
Nov
5
Lec22: CTMC: Chapman-Kolmogorov Equations (6.4) 7
Lec23: : CTMC: Limiting Probabilities (6.5)
9
Lec24: CTMC: Computing the Transition Probabilities (6.8)
Nov
13
Fall Break 15
 Fall Break 17
Fall Break
Nov
19
Lec25: Renewal Theory: Intro (7.1), Renewal Process, Properties.
21
Lec26:  Renewal Theory: Some Distributions (7.2), Renewal Equation. 
Limit Theorems (Optional)(7.3)
23
Lec27: Brownian Motion (BM) (10.1);Variations and Martingales Properties (10.3)
Nov
26
Quiz#2 (based on Lectures 20-27)
28
Lec28:  BM: Pricing Stock Options and Black-Scholes Formula (10.4.1-10.4.2) 30
Lec29: BM: Black-Scholes Formula's Derivation
Dec
3
Lec30: BM: Black-Scholes Formula's Interpretation
5
Lec31: Stationary Processes (10.7) 7
Lec32: Simulation Methods (11.2-11.3) 
Table of Random Digits



Announcements: 

Final Exam: Tuesday, December 11, 7pm-9pm, KN DANCE (KNA 163)
(Office Hours: Monday, Dec 10, 1pm-3pm, MS 552)
(Bring in Your ID Card)

It will cover all the materials covered in this course.
Formula Sheet for Final Exam and Two Tables
(Normal Distribution and Exponential Funaction)
Basic Calculator is Allowed
*
Your Marks: Q1&Q2&Midterm (Excel)
*
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 7, 2018.