• Class Number 4237
  • Term Code 2930
  • Class Info
  • Unit Value 6 units
  • Mode of Delivery In Person
    • Dr Yuguang Ipsen
    • Dr Yuguang Ipsen
  • Class Dates
  • Class Start Date 25/02/2019
  • Class End Date 31/05/2019
  • Census Date 31/03/2019
  • Last Date to Enrol 04/03/2019
SELT Survey Results

This course introduces students to the theory of basic discrete and continuous time Markov processes and also Gaussian processes including Brownian motion and related processes.
Topics include: Review of random variable characterisations, including cumulative distribution functions, probability density and mass functions, moment generating functions, joint, marginal and conditional distributions and conditional expectations and variances; Markov chains, including state-space decomposition, first-step analysis and determination of stationary and steady state distributions; Markov jump process theory, including embedded Markov chains, homogeneous and inhomogeneous Poisson processes and birth and death processes; Gaussian processes, including Brownian motion, geometric Brownian motion, Brownian bridges, integrated Brownian motion and White Noise.

Research-Led Teaching

The course provides the up-to-date introduction in the mathematical underpinning of modern prob- ability theory, that is the mathematical theory of uncertainty. Contrived in the 20 century, it is the foundation of any modern research in the area of probability and stochastic processes. Apart from this, it provides useful tools in any area of research dealing with reasoning and uncertainty such as as mathematics, statistics, economics, finance, computer science and engineering.

Examination Material or equipment

Mid-Semester Exam

·        one sheet of A4 paper with handwritten notes only on both sides

·        paper-based dictionary, no approval required (must be clear OF ALL annotations)

·        calculator (any - programmable or not)

Final Exam

·        two sheets of A4 paper with handwritten notes only on both sides

·        paper-based dictionary, no approval required (must be clear OF ALL annotations)

·        calculator (any - programmable or not)


Required Resources

Prescribed Text

Jeffrey S. Rosenthal (2008) A First Look at Rigorous Probability Theory. 2nd Edition. World Scientific, Singapore.

 Available at loan desk for 2 hour loan at Hancock library.

Recommended Reading

George G Roussas (2014) An Introduction to Measure-Theoretic Probability. 2nd Edition. Academic Press

Rick Durrett (2010) Probability: Theory & Examples. 4th Edition. Cam- bridge. University Press, Cambridge.

Davar Khoshnevisan (2007) Probability. American Mathematical Society. Providence,RI.

Sidney I. Resnick (2015) A probability path. Reprint of the fifth (2005) printing of the 1999 original. Birkhaeuser/Springer, New York.

Daniel W. Stroock (2013) Mathematics of Probability. American Mathematical Society, Providence. David Williams (1991) Probability with Martingales. Cambridge University Press, Cambridge.

Staff Feedback

Student feed back will be given in the following forms in this course:

• Written comments, both individually and to the whole class.

• Verbal comments to the whole class.

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.

Other Information

Consultation time will be finalised at the start of the semester.


Your final mark for the course will be based on the raw marks allocated for each of your assess- ment items. However, your final mark may not be the same number as produced by that formula, as marks may be scaled. Any scaling applied will preserve the rank order of raw marks (i.e. if your raw mark exceeds that of another student, then your scaled mark will exceed the scaled mark of that student), and may be either up or down.

Referencing Requirements

Appropriate referencing will be necessary for the Assignments. For more information see: http//www.anu.edu.au/students/learning - development/academic - integrity/how - referencing - works

Extensions and Penalties

No submission of assessment tasks without an extension after the due date will be permitted. If an assessment task is not submitted by the due date, a mark of 0 will be awarded.

Support for Students

The University offers a number of support services for students. Information on these is available online from http : //students.anu.edu.au/studentlife/?

Class Schedule

Week/Session Summary of Activities Assessment
1 the need for measure theory
2 probability triples
3 sequence and random variables and independence
4 limit and tail fields
5 expectation and integration online quiz (5%)
6 inequalities and convergence
7 distribution of random variables mid semester exam (20%)
8 some limit theorems
9 weak convergence
10 characteristic functions
11 decomposition of probability laws
12 conditional probability and expactation

Tutorial Registration

Tutorial signup for this course will be done via the Wattle website. Detailed information about signup times will be provided on Wattle or during your first lecture. When tutorials are available for enrolment, follow these steps:


1.   Log on to Wattle, and go to the course site

2.   Click on the link ‘Tutorial enrolment’

3.   On the right of the screen, click on the tab ‘Become Member of . . . .’ for the tutorial class you wish to enter

4.   Confirm your choice


If you need to change your enrolment, you will be able to do so by clicking on the tab ‘Leave group. . . .’ and then re-enrol in another group. You will not be able to enrol in groups that have reached their maximum number. Please note that enrolment in ISIS must be finalised for you to have access to Wattle.

Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Online Quiz (optional and redeemable) 5 % 29/03/2019 29/03/2019 1,2,3
Mid Semester Exam (optional and redeemable) 20 % 01/04/2019 03/05/2019 1,2,3,4
Final Exam (compulsory) 75 % 06/06/2019 04/07/2019 1,2,3,4

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


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:

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 ANU Online website. Students may choose not to submit assessment items through Turnitin. In this instance you will be required to submit, alongside the assessment item itself, hard copies of all references included in the assessment item.

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.


As a further academic integrity control, students may be selected for a 15 minute individual oral examination of their written assessment submissions.

Any student identified, either during the current semester or in retrospect, as having used ghost writing services will be investigated under the University’s Academic Misconduct Rule. 

Assessment Task 1

Value: 5 %
Due Date: 29/03/2019
Return of Assessment: 29/03/2019
Learning Outcomes: 1,2,3

Online Quiz (optional and redeemable)

Students are presented with 5 quiz questions online in Week 5 to be attempted within one hour. Feedback will be returned immediately after attempting the quiz. The quiz is redeemable and optional.

Value : 5% of the Final Raw Mark

Estimated return date: same day

Assessment Task 2

Value: 20 %
Due Date: 01/04/2019
Return of Assessment: 03/05/2019
Learning Outcomes: 1,2,3,4

Mid Semester Exam (optional and redeemable)

Materials taught before the mid-semester exam will be assessed. The mid-semester exam is redeemable and optional. Students are strongly encouraged to sit for the mid-semester exam.

Due date: The expected date is between Week 6 to Week 7. The specific date will be announced later by the examination office.

Value: 20% of the Final Raw Mark

Estimated return date: 1 – 2 weeks after the exam. In the case of deferred exam, the return date will be postponed until 1 week after the deferred exam.

Assessment Task 3

Value: 75 %
Due Date: 06/06/2019
Return of Assessment: 04/07/2019
Learning Outcomes: 1,2,3,4

Final Exam (compulsory)

The compulsory final exam assesses the students’ overall learning outcomes.

Value: 75% of the Final Raw Mark

Academic Integrity

Academic integrity is a core part of our culture as a community of scholars. At its heart, academic integrity is about behaving ethically. This means that all members of the community commit to honest and responsible scholarly practice and to upholding these values with respect and fairness. The Australian National University commits to embedding the values of academic integrity in our teaching and learning. We ensure that all members of our community 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 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 University has policies and procedures in place to promote academic integrity and manage academic misconduct. Visit the following Academic honesty & plagiarism website for more information about academic integrity and what the ANU considers academic misconduct. The ANU offers a number of services to assist students with their assignments, examinations, and other learning activities. The Academic Skills and Learning Centre offers a number of workshops and seminars that you may find useful for your studies.

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) as 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 assessment tasks without an extension after the due date will be permitted. If an assessment task is not submitted by the due date, 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 returned online.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. The Course Convener may grant extensions 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

Assignments may not be resubmitted.

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).

Dr Yuguang Ipsen

Research Interests

Levy processes, combinatorial stochastic processes, machine learning, computational biology

Dr Yuguang Ipsen

Monday 00:00 00:00
Monday 00:00 00:00
Dr Yuguang Ipsen

Research Interests

Dr Yuguang Ipsen

Monday 00:00 00:00
Monday 00:00 00:00

Responsible Officer: Registrar, Student Administration / Page Contact: Website Administrator / Frequently Asked Questions