An introduction to stochastic processes, which are random processes occurring in time or space.

They are used to model dynamic relationships involving random events in a wide variety of disciplines including the natural and social sciences, and in financial, managerial and actuarial settings.

The course consists of a short review of basic probability concepts and a discussion of conditional probability and conditional expectation, followed by an introduction to the basic concepts and an investigation of the long-run behaviour of Markov chains in discrete time, countable state space. The course also covers some important continuous-time stochastic processes including Poisson processes and other Markov pure jump processes, as well as Brownian motion and other related Gaussian processes as time permits.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Describe basic concepts of stochastic processes in discrete time, especially concerning Markov chains, their classifications and long-run behaviour; and
2. Demonstrate an understanding of continuous-time stochastic processes, with topics drawn from: Poisson Processes Other Markov pure jump processes Brownian motion Other related Gaussian processes

Research-Led Teaching

ANU has a rich history of research in the area of applied probability and stochastic processes. The lecturer and other RSFAS staff members are active researchers in this area, with a keen interest in attracting talented students for research projects.

Examination Material or equipment

You will require reliable access to Wattle and a calculator for the duration of the online exam. You may use R for numerical calculations if you wish.

Required Resources

All required course materials will be made available on Wattle.

Recommended Resources

The lecture notes have been designed to be self-contained and consequently purchase of textbooks is OPTIONAL. The course material follows selectively:

• Introduction to Probability Models (11th Edition, 2014) by Sheldon Ross, available as ebook through ANU library at http://library.anu.edu.au/record=b3573439.

Other examples of relevant texts are (these are both available in the Hancock library and are available on a 2-hour reserve):

• A First Course in Stochastic Processes (1975) by S. Karlin and H.M. Taylor
• Markov Chains (1997) by J.R. Norris

Staff Feedback

Students will be given feedback in the following forms in this course:

• written comments
• verbal comments
• feedback to whole class, groups, individuals, focus groups etc.

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Revision of Elementary Probability Theory
2	Random Variables
3	Conditional Probability and Conditional Expectation	Assessment 1 to be released
4	Markov Chains 1
5	Markov Chains 2	Assignment 1 due
6	Markov Chains 3	Assessment 2 to be released
7	The Exponential Distribution and Poisson Processes 1
8	The Exponential Distribution and Poisson Processes 2	Assignment 2 due
9	Continuous-time Markov Chains 1	Assessment 3 to be released
10	Continuous-time Markov Chains 2
11	Brownian Motion, Gaussian Processes and Stationarity 1	Assignment 3 due
12	Brownian Motion, Gaussian Processes and Stationarity 2

Tutorial Registration

Tutorials will be available on campus, live through scheduled Zoom sessions and as pre-recorded videos. Information regarding enrolments for these options will be provided on Wattle during Week 0 of the semester.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignment 1	10 %	27/08/2021	03/09/2021	1
Assignment 2	10 %	01/10/2021	15/10/2021	1
Assignment 3	10 %	22/10/2021	29/10/2021	2
Final Examination	70 %	04/11/2021	02/12/2021	1,2

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Integrity . In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

Course content delivery will take the form of pre-recorded weekly lectures (available via echo360 on Wattle), pre-recorded weekly workshops (available via echo360 on Wattle) and weekly tutorials, delivered in hybrid format (on campus, live through scheduled Zoom sessions and as pre-recorded videos).

 

Examination(s)

The exam will be centrally scheduled though Examinations, Graduations & Prizes and will be timetabled prior to the Semester 2 examination period. Please check ANU Timetabling for further information.

Assessment Task 1

Assignment 1

Provide detailed solutions to questions based on material from Weeks 1 to 3. Assignment 1 will be made available on Wattle before 3pm on Friday 13 August 2021 and will be due before 3pm on Friday 27 August 2021. When completed, solutions to Assignment 1 (including the declaration sheet) should be submitted to Wattle in a single pdf file. Options for producing this pdf file are: (i) using a text processing package such as latex to produce a pdf document; or (ii) scanning hand-written solutions into a pdf document; or (iii) photographing hand-written solutions into a pdf document. If you use options (ii) or (iii), please ensure that your handwriting is legible. Assignments will be graded and marks will be returned via Wattle.

Assessment Task 2

Assignment 2

Provide detailed solutions to questions based on material from Weeks 4 to 6. Assignment 2 will be made available before 3pm on Friday 17 September 2021 and will be due before 3pm on Friday 1 October 2021. Details concerning the submission of your solutions and return of the marks are the same as for Assignment 1.

Assessment Task 3

Assignment 3

Provide detailed solutions to questions based on material from Weeks 7 to 10. Assignment 3 will be made available before 3pm on Friday 8 October 2021 and will be due before 3pm on Friday 22 October 2021. Details concerning the submission of your solutions and return of the marks are the same as for Assignment 1.

Assessment Task 4

Final Examination

The final examination will be a Wattle-based online exam during the university examination period at the end of the semester. The exam will be 3 hours long (plus 15 minutes reading time plus 15 minutes online submission time) and will cover the entire syllabus. It will be open book and all materials are permitted. The exam will be centrally timetabled and details of the final examination timetable will be made available on the ANU Timetabling website.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

No submission of assignments after the due date will be permitted without an extension approved before the deadline. If an assignment is not submitted by the due date, and no extension has been approved, a mark of 0 will be awarded.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

Assignments will be graded and marks will be returned via Wattle.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

No resubmission of assignments is permitted.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students