STAT 761 L01 (Winter 2015)
"Stochastic Processes"
Course Outline
Instructor:
Anatoliy Swishchuk
E-mail: aswish@ucalgary.ca
Office: MS552
Tel.: (403) 220-3274
Office Hours: MW:12-1pm

Place: MS452

Lectures Schedule for  Stat 761
Lectures schedule (L01)
Monday/Wednesday:1:00-1:50pm (MS452)/Friday: 2:00-2:50pm (MS371)

Syllabus
Elements of Stochastic Processes, Markov chains, Renewal processes, Martingales, Brownian motion, Branching processes, Stationary processes, Diffusion processes, Levy processes

Course Information Sheet
 Important Class Dates:
First day of class: 13:00, Monday, January 12, 2015
  A# 1: Feb 9, Mon, 13:50 (MS452)
  A# 2: Mar 2, Mon, 13:50 (MS452)
    A# 3: Mar 23, Mon, 13:50 (send pdf-file to: aswish@ucalgary.ca)
   A# 4: Apr 15, Wed, 13:50 (MS452)
         Last day of class: April 15, Wed, 2015.
 
Project Due:
Wednesday, April 15, 2015, 13:50, MS452

Recommended textbooks:
'A First Course in Stochastic Processes' by S. Karlin and H. Taylor, 2nd ed., Academic Press, 1975

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 (http://math.ucalgary.ca/courses/w11).
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://www.math.ucalgary.ca/~aswish/stat761W15.html/

Class work:
In-class lectures with typical examples (short lecture notes will be posted on the webpage in the form of pdf-files
);
your computer must have an Adobe Acrobat reader (for free downloading see www.adobe.com).

Assignments and Project
There will be 4 Assignments and 1 Project

Grading scheme (Course Evaluation) for STAT761 Winter2015

Assignments (4)
60%=4x15% (15% for each assignments)
A1: Feb 9; A2: Mar 2; A3: Mar 23 (send pdf-file to: aswish@ucalgary.ca); A4: Apr 15 (1:50am) (in-class)
Project 40%  Wednesday, April 15, 2015, 13:50, MS452
Tentative Lectures Schedule for STAT761 Winter 2015
Month
Day
Monday Day
Wednesday Day
Friday
Jan
12
Lec1:  Introduction: Course outline; Elements of stochastic processes: review of basic terminology, two simple examples
14
Lec2: Elements of stochastic processes: classification, definition
16
Lec3: Markov Processes, Semigroups and Generators
Jan
19
Lec4: Markov Chains (MC): definitions, transition probabilities matrices, examples
21
Lec5: MCs: classification of states, basic limit theorem of Markov chains
23
Lec6: MC: finite state continuous time MC
Jan
26
Lec7: Renewal Processes(RP):  definition, examples
28
Lec8:  RP: Renewal Equations
30
Lec9: RP: Renewal Theorems
Feb
2
Lec10: RP: Variations of RP (Delayed, Stationary, CLT,etc.) 4
Lec11: Martingales: definition, examples, supermartingales and submartingales (discrete time)
6
Lec12: Martingales (sub- and supermartingales): continuous time
Feb
9
Lec13:  Martingales: The Optional Stopping Theorem (OST); Applications of OST 11
Lec14: Martingales: applications to discrete-time (B,S)-security markets (finance) 13
Lec15:  Brownian Motion (BM): background, joint probabilities
Feb
16
Reading Week (No Lectures) 18
Reading Week (No Lectures)
20
 Reading Week (No Lectures)
Feb
23
 Lec16:  BM: continuity of paths, reflection principle and the maximum value 25
 Lec17:  Miltidimensional BM: Definition, 2-D BM.
27
  Lec18: BM:  Variations of BM and Extensions
Mar
2
Let19: BM: martingale methods 4
Lec20: BM: Laplace Transform and Application in Finance (Perpetual Warrant) 6
Lec21: Branching Processes (BP):  Examples,  pure birth, birth and death processes
Mar
9
Lec22:  BP: generating function relation for BP
11
Lec23: BP: extinction probabilities, martingale properties
13
Lec24: BP: continuous-time, extinction probabilities
Mar
16
Lec25:  Stationary Processes(SP): definition, examples 18
Lec26: SP: Mean Square Error Prediction
20
Lec27: SP: The Prediction Theorems and Examples
Mar
23
Lec28: SP: Ergodic Theory for SP 25
Lec29: Diffusion Processes (DP): definition, examples 27
Lec30: DP: definition, examples II /Existence and Uniqueness Theorem
Mar-Apr
30
Lec31: DP: Existence and Uniqueness Theorem /Ito Formula 1
Lec32: DP: Ito formula /Integration by Parts Formula
3
Good Friday (No Lecture)
Apr
6
Lec33:  DP: Integration by Parts Formula/ Girsanov's Theorem 8
Lec34: DP: Applications in Finance, (B,S)-Security Markets, Risk-Neutral Measure 10
Lec35:  Levy Processes (LP): definition,  examples, infinite divisibility
Apr
13
Lec36: LP: Levy-Khintchine Formula 15
Lec37: LP: Poisson Measure and Integral I
(Lec38 (Appendix): Levy-Ito Decomposition)

Enjoy the Levy Processes!


Announcements: 

Assignment#4: Due-Wed, April 15, 2015 (in-class)
Assignment#3: Due-Monday, March 23, 2015, 2pm (send pdf-file to: aswish@ucalgary.ca)

Assignment#2: Due-Monday, March 2, 2015 (in-class)

Assignment#1: Due-Monday, February 9, 2015 (in-class)
Assignment Policy
Projects in Stochastic Processes (Due-Wednesday (In-class), April 15, 2015, MS452)
(Project is a Homework Assignment (see Assignment Policy above))


This page was updated on April 15, 2015.