STAT 761 L01 (Winter 2011)
"Stochastic Processes"
Course Outline
Instructor:
Anatoliy Swishchuk
E-mail: aswish@ucalgary.ca
Office: MS552
Tel.: (403) 220-3274
Office Hours: MW:10-11am

Place: MS569

Lectures Schedule for  Stat 761
Lectures schedule (L01)
Monday:11:00-11:50am; Wednesday: 8:00-8:50am; 11:00-11:50pm (MS569)

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: 11:00am, Monday, January 10, 2011
  A# 1: Feb 7, Mon, 11:50 (MS569)
  A# 2: Mar 7, Mon, 11:50 (MS569)
    A# 3: Mar 28, Mon, 11:50 (MS569)
   A# 4: Apr 13, Wed, 11:50 (MS569)
         Last day of class: April 13, Fri, 2011.
 
Project Due:
Monday, April 18, 2011, noon, MS552

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/stat761W11.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 Winter2011
Assignments (4)
60%=4x15% (15% for each assignments)
A1: Feb 7; A2: Mar 7; A3: Mar 28; A4: Apr 13(11:50am) (in-class)
Project 40%  Monday, April 18, 2011, noon, MS552

Tentative Lectures Schedule for STAT761 Winter 2011
Month
Day
Monday (11am)
Day
Wednesday (8am)
Day
Wednesday (11am)
Jan
10
Lec1:  Introduction: Course outline; Elements of stochastic processes: review of basic terminology, two simple examples
12
Lec2: Elements of stochastic processes: classification, definition
12
Lec3: Markov Chains (MC): examples, transition probabilities
Jan
17
Lec4: MC: transition probabilities matrices, classification of states, recurrence
19
Lec5: MCs: basic limit theorem of Markov chains
29
Lec6: MC: finite state continuous time MC
Jan
24
Lec7: Renewal Processes(RP):  definition, examples
26
Lec8:  RP: Renewal Equations
26
Lec9: RP: Renewal Theorems
Jan-Feb
31
Lec10: RP: Variations of RP (Delayed, Stationary, CLT,etc.) 2
Lec11: Martingales: definition, examples, supermartingales and submartingales (discrete time)
2
Lec12: Martingales (sub- and supermartingales): continuous time
Feb
7
Lec13:  Martingales: The Optional Sampling Theorem (OST); Applications of OST 9
Lec14: Martingales: applications to discrete-time (B,S)-security markets (finance) 9
Lec15:  Brownian Motion (BM): background, joint probabilities
Feb
14
Lec16:  BM: continuity of paths, reflection principle and the maximum value
16
Lec17:  BM:  Variations of BM and Extentions 16
 Lec18: BM: martingale methods
Feb
21
  Reading Week (No Lectures)
23
  Reading Week (No Lectures) 23
  Reading Week (No Lectures)
Feb-Mar
28
Let19: BM: Laplace Transform and Application in Finance (Perpetual Warrant)
2
Lec20: Miltidimensional BM: Definition, 2-D BM.
2
Lec21: Branching Processes (BP):  Examples,  pure birth, birth and death processes
Mar
7
Lec22:  BP: generating function relation for BP
9
Lec23: BP: extinction probabilities, martingale properties
9
Lec24: BP: continuous-time, extinction probabilities
Mar
14
Lec25:  Stationary Processes(SP): definition, examples 16
Lec26: SP: Mean Square Error Prediction
16
Lec27: SP: The Prediction Theorems and Examples
Mar
21
Lec28: SP: Ergodic Theory for SP 23
Lec29: Diffusion Processes (DP): definition, examples 23
Lec30: DP: definition, examples II /Existence and Uniqueness Theorem
Mar-Apr
28
Lec31: DP: Existence and Uniqueness Theorem /Ito Formula 30
Lec32: DP: Ito formula /Integration by Parts Formula 30
Lec33:  DP: Integration by Parts Formula/ Girsanov's Theorem
Apr
4
Lec34: DP: Applications in Finance, (B,S)-Security Markets, Risk-Neutral Measure
6
Lec35:  Levy Processes (LP): definition, examples, infinite divisibility 6
Lec36: LP: Levy-Khintchine Formula
Apr
11
Lec37: LP: Poisson Measure and Integral I 13
Lec38: LP: Poisson Measure and Integral II 13
Lec39: LP: Levy-Ito Decomposition/Applications (finance)


Announcements: 

Your Final Marks are available now:
send me e-mail (aswish@ucalgary.ca) to know your mark.


Assignment#4: Due-Wed, April 13, 2011 (in-class)

Assignment#3: Due-Monday, March 28, 2011 (in-class)

Assignment#2: Due-Monday, March 7, 2011 (in-class)

Assignment#1: Due-Monday, February 7, 2011 (in-class)
Assignment Policy
Projects in Stochastic Processes (Due-Monday(Noon), April 18, 2011, MS552)
(Project is a Homework Assignment (see Assignment Policy above))


This page was updated on April 20, 2011.