- Class Number 5983
- Term Code 3160
- Class Info
- Unit Value 6 units
- Mode of Delivery In Person
- AsPr Boris Buchmann
- AsPr Boris Buchmann
- Class Dates
- Class Start Date 26/07/2021
- Class End Date 29/10/2021
- Census Date 14/09/2021
- Last Date to Enrol 02/08/2021
The course offers an introduction to modern stochastic processes, including Brownian motion, continuous-time martingales, stochastic integration and Ito's calculus, Markov processes, stochastic differential equations, point processes and their applications. The course will include some applications but will emphasise setting up a solid theoretical foundation for the subject.
The course will provide a sound basis for progression to other honours and post-graduate courses including mathematical finance, stochastic analysis and statistics, and actuarial sciences.
The course aims to round off the rigorous introduction to probabilistic reasoning initiated in STAT7018, as well as to substantially enhance students' depth of knowledge in the mathematical underpinning of stochastic process theory.
Upon successful completion, students will have the knowledge and skills to:
- Explain in detail the fundamental concepts of stochastic processes in continuous time and their position in modern statistical and mathematical sciences and applied contexts;
- Demonstrate accurate and efficient use of complex stochastic calculus techniques;
- Demonstrate in depth capacity for mathematical reasoning through analysing, proving and explaining concepts from stochastic analysis; and
- Apply complex problem-solving techniques using stochastic analysis methods in various situations.
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 to attract talented students for research projects.
Examination Material or equipment
Lecture Notes will be made available through Wattle on a weekly basis.
The following book is available an as e-book.
Klebaner, Fima C. (2012) Introduction to stochastic calculus with applications. Third Edition. Imperial College Press, London.
Preliminary Reading (STAT3004). Rosenthal, Jeffrey S. (2008) A first look at rigorous probability theory.
2nd edition, World Scientific, Singapore. https://ebookcentral.proquest.com/lib/anu/detail.action?docID=5227675
The following books are made available as hard copies in the two hours reserve of the Hancock library.
Revuz, Daniel; Yor, Marc (1990) Continuous Martingales and Brownian Motion. 2nd ed, Springer, Berlin.
Students will be given feedback in the following forms in this course:
- Written comments
- Verbal comments
- Feedback to the whole class
- Assignment 1 and 2
Student FeedbackANU 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.
|Week/Session||Summary of Activities||Assessment|
|5||Brownian motion: existence and properties|
|6||Brownian motion: existence and properties|
|7||Stochastic integration and Stochastic differential equations||Assignment 1 due|
|8||Stochastic integration and Stochastic differential equations||Assignment 1 returned|
|9||Stochastic integration and Stochastic differential equations|
|10||Stochastic integration and Stochastic differential equations|
|11||Optional topics (some of the following ): diffusion, point processes, Levy processes, etc||Assignment 2 due|
|12||Optional topics (some of the following ): diffusion, stationary point processes, Levy processes. etc||Assignment 2 returned|
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 O-week, prior to the start of the semester.
|Assessment task||Value||Due Date||Return of assessment||Learning Outcomes|
|Assignment 1||20 %||24/09/2021||01/10/2021||1-2|
|Assignment 2||20 %||22/10/2021||29/10/2021||3-4|
|Assignment 3||60 %||19/11/2021||02/12/2021||1-4|
* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details
PoliciesANU 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 RequirementsThe 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 AssessmentMarks 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.
Course content delivery will take the form of pre-recorded weekly lectures (available via echo360 on Wattle) and weekly tutorials, delivered in hybrid format (on campus, live through scheduled Zoom sessions and as pre-recorded videos).
Centrally administered examinations through Examinations, Graduations & Prizes will be timetabled prior to the examination period. Please check ANU Timetabling for further information.
Assessment Task 1
Learning Outcomes: 1-2
Assignment 1 covers topics from weeks 1-4. The problems will be made available at least two weeks prior to submission. You may type your answer in a type-setting software or you may hand-write parts of your answers. Please ensure that your handwriting is legible. Assignment 1 is due no later than 23:59 AEST on the due date via Wattle (Turnitin) link. If an assessment task is not submitted by the due date, a mark of 0 will be awarded. This assignment is to be completed individually and can only be submitted once.
Assessment Task 2
Learning Outcomes: 3-4
Assignment 2 covers topics covered from weeks 5-10. The problems will be made available at least two weeks prior to submission. You may type your answer in a type-setting software or you may hand-write parts of your answers. Please ensure that your handwriting is legible. Assignment 2 is due no later than 23:59 AEST on the due date via Wattle (Turnitin) link. If an assessment task is not submitted by the due date, a mark of 0 will be awarded. This assignment is to be completed individually and can only be submitted once.
Assessment Task 3
Learning Outcomes: 1-4
The final assignment will be based on all work throughout the semester (i.e. the entire syllabus) and will be submitted via Wattle. The assignment is to be completed individually and students will have only one attempt to submit their solutions. The assignment will be released on Friday, November 12 (12:30pm) and due on Friday, November 19 (12:30pm).
Academic IntegrityAcademic 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.
The ANU uses 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. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.
There are no hardcopy submissions in this course.
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 RequirementsAccepted 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.
Assignments will be returned via Wattle.
Extensions and PenaltiesExtensions 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
Resubmission of assignments is not allowed.
Distribution of grades policyAcademic 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 studentsThe 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
Probability theory, stochastic processes, limit theory, Levy processes, inference and mathematical finance
AsPr Boris Buchmann