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. Articulate basic concepts of stochastic processes in discrete time, especially concerning Markov chains, their classifications and long-run behaviour; and
2. Critically analyse continuous-time stochastic processes, with topics drawn from Poisson processes, other Markov pure jump processes, Brownian motion and 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 access to a non-programable calculator during the exam.

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. No particular book is recommended but there are many books that contain relevant material, including:

• Introduction to Probability Models (11th Edition, 2014) by Sheldon Ross, available as an ebook through ANU library at http://library.anu.edu.au/record=b3573439
• A First Course in Stochastic Processes (1975) by S. Karlin and H.M. Taylor, available in the Hancock Library on a 2 hour reserve
• Markov Chains (1997) by J.R. Norris, available in the Hancock Library on a 2 hour reserve

Staff Feedback

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

• written comments (e.g. a summary on Wattle of class performance in each assignment)
• verbal comments (e.g. during live workshops and tutorials)
• individual verbal comments upon request (e.g. during office 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	Revision of Elementary Probability Theory
2	Random Variables	Tutorials commence
3	Conditional Probability and Conditional Expectation	Assessment 1 to be released on 11 August 2023 before 5pm
4	Markov Chains 1
5	Markov Chains 2	Assignment 1 due on 25 August 2023 before 5pm
6	Markov Chains 3	Assessment 2 to be released on 1 September 2023 before 5pm
7	The Exponential Distribution and Poisson Processes 1
8	The Exponential Distribution and Poisson Processes 2	Assignment 2 due on 29 September 2023 before 5pm
9	Continuous-time Markov Chains 1	Assessment 3 to be released on 6 October 2023 before 5pm
10	Continuous-time Markov Chains 2
11	Brownian Motion, Gaussian Processes and Stationarity	Assignment 3 due on 20 October 2023 before 5pm
12	Applications to Actuarial Studies

Tutorial Registration

Tutorials will be available on campus in person. Information regarding enrolments for these options will be provided on MyTimetable during Week 0 of the semester. ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage (https://www.anu.edu.au/students/program-administration/timetabling).

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignment 1	10 %	25/08/2023	31/08/2023	1
Assignment 2	10 %	29/09/2023	13/10/2023	1
Assignment 3	10 %	20/10/2023	27/10/2023	2
Final Examination	70 %	02/11/2023	30/11/2023	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 3 hours of in-person lectures per week which will be recorded and subsequently made available via Echo360 on Wattle. In addition there will be a one hour workshop per week in person which will be recorded and subsequently made available via Echo360 on Wattle. The workshops will typically be student-led rather than lecturer-led and will provide plenty of opportunity to ask questions about, and discuss the contents of the course. Attendance and participation in lectures, workshops and tutorials is recommended but is not assessed.

Examination(s)

The end-of-semester examination 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 5pm on Friday 11 August 2023 and will be due on Friday 25 August 2023 before 5pm. 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 5pm on Friday 1 September 2023 and will be due on Friday 29 September 2022 before 5pm. Details concerning the submission of your solutions are the same as for Assignment 1. Assignments will be graded and marks will be returned via Wattle.

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 5pm on Friday 6 October 2023 and will be due on Friday 20 October 2023 before 5pm. Details concerning the submission of your solutions are the same as for Assignment 1. Assignments will be graded and marks will be returned via Wattle.

Assessment Task 4

Final Examination

The final examination will be an in-person exam during the university examination period at the end of the semester. The exam will be 3 hours long (plus 15 minutes reading time) and will cover the entire syllabus. The exam will be centrally timetabled and 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. 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

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 by the Convenor 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

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.

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 Access 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 all ANU students