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. Decsribe in detail the basic concepts of stochastic processes in discrete time, especially concerning Markov chains, their classifications and long-run behaviour; and
2. Explain in detail continuous-time stochastic processes, with topics drawn from:            Poisson Processes            other Markov pure jump processes            Brownian motion           Other related Gaussian processes

Research-Led Teaching

Although the material in this course may be considered classical, the course will be taught through a modern lens and illuminated by recent research in stochastic processes.

Examination Material or equipment

Only a non-programmable calculator is allowed.

Required Resources

All required course materials will be made available on the course page.

Recommended Resources

Purchase of textbooks is not required for this course. Textbooks are available through the ANU Library, including:

• Lawler, G.F. Introduction to Stochastic Processes (2006)
• Karlin, S. and Taylor, H.M. A First Course in Stochastic Processes (1975)
• Norris, J. Markov Chains (1997)
• Ross, S. Introduction to Probability Models (2019)

Staff Feedback

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

• written feedback to three assignments
• verbal feedback from tutors during tutorials and consultation hours
• verbal feedback from the lecturer to the whole class during lectures and individually during consultation hours

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). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Review of elementary probability theory
2	Conditional probability and conditional expectation
3	Markov chains
4	Classification of Markov chains	Assignment 1 due
5	Long-run behaviour of Markov chains
6	More on discrete-time stochastic processes
7	Poisson processes	Assignment 2 due
8	Continuous-time Markov chains
9	Random walk
10	Brownian motion
11	Gaussian processes	Assignment 3 due
12	More on continuous-time stochastic processes

Tutorial Registration

Tutorial registration will be available via ANU Timetabling two weeks prior to the beginning of the semester and will close on Friday of Week 3.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignment 1	10 %	14/08/2024	28/08/2024	1
Assignment 2	10 %	18/09/2024	02/10/2024	1
Assignment 3	10 %	16/10/2024	30/10/2024	2
Final Examination	70 %	31/10/2024	28/11/2024	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 Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Extenuating Circumstances Application
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

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 Skills website. 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 weekly in-person lectures and weekly in-person tutorials on campus. Attendance at lectures and tutorials, while not compulsory, is expected in line with paragraph 2(b) of the ANU Code of Practice for Teaching and Learning. There will be weekly drop-in sessions with the lecturer and tutors for student consultation.

Examination(s)

Centrally scheduled examinations through Examinations, Graduations & Prizes will be timetabled prior to the examination period. Please check ANU Timetabling for further information.

Assessment Task 1

Assignment 1

This assignment is to be done individually. The assignment questions, which typically involve a mix of ‘pen-and-paper’ and computational tasks, will be released two weeks before the due date and will cover material that has been seen in previous lectures. Assignment scripts must be submitted via Wattle by midday on the due date and will be returned on the 'Return of Assessment Date'. Any assignment submitted late without an extension approved prior to the assignment deadline will receive a mark of zero.

Assessment Task 2

Assignment 2

This assignment is to be done individually. The assignment questions, which typically involve a mix of ‘pen-and-paper’ and computational tasks, will be released two weeks before the due date and will cover material that has been seen in previous lectures. Assignment scripts must be submitted via Wattle by midday on the due date and will be returned on the 'Return of Assessment Date'. Any assignment submitted late without an approved extension will receive a mark of zero.

Assessment Task 3

Assignment 3

This assignment is to be done individually. The assignment questions, which typically involve a mix of ‘pen-and-paper’ and computational tasks, will be released two weeks before the due date and will cover material that has been seen in previous lectures. Assignment scripts must be submitted via Wattle by midday on the due date and will be returned on the 'Return of Assessment Date'. Any assignment submitted late without an approved extension will receive a mark of zero.

Assessment Task 4

Final Examination

The final examination will be 3 hours long and cover the entire course. It will be invigilated, in person, on campus during the final examination period. The timetable will be made available on the ANU Examination Timetable website.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

Assessment pieces are to be submitted online via Wattle. Please keep a copy of tasks completed for your records. 

Hardcopy Submission

Assignments are to be submitted online via Wattle. If you are unable to submit an assignment online, you must bring this to the attention of the course convenor well in advance of the assignment due date.

Late Submission

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

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material. Any use of artificial intelligence must be properly referenced. Failure to properly cite use of Generative AI will be considered a breach of academic integrity.

Returning Assignments

Assignments will be returned via Wattle. Students are encouraged to use the consultation time of the tutor and lecturer to obtain further feedback if necessary.

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 Accessibility 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 supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents all ANU students