General Course Information

Course Code :  MATH5835

Year :  2024

Term :  Term 1

Teaching Period :  T1

Course Details & Outcomes

Course Description

This is a Postgraduate level course in Stochastic Processes for students in Mathematics and

Statistics. The theory of stochastic processes deals with phenomena evolving randomly in time and/or space, such as prices on fnancial markets, air temperature or wind velocity, spread of

diseases, number of hospital admissions in certain area, and many others. This course

introduces some of the basic ideas and tools to study such phenomena. In particular, we will

introduce the concept of martingale to study phenomena evolving in discrete time and the

concept of Poisson process (and its generalizations) and Brownian Motion to study processes   evolving continuously in time. Some applications to statistical inference will also be discussed.  The course will also equip you with the foundational knowledge for more advanced courses in    the Master of Financial Mathematics program. There will be four hours of lectures and one hour of tutorial/consultation each week.

Pre-requisites: 24 units of level III mathematics (including 6 units in MATH3801 Probability and

Stochastic Processes or MATH3901 Higher Probability and Stochastic Processes or an equivalent course) or a degree in a numerate discipline or permission of the Head of Department.

Course Aims

The aim of this course is to introduce some of the foundational ideas and tools of the theory of

stochastic processes. The course features the fundamental concepts of measure and

probability, integral and expectation, conditional expectation, independence, special dependence structures such as martingales and Markov processes, and some basic continuous processes    such as Poisson processes and Brownian motion. In addition to familiarise students with the

basic types of stochastic processes often encountered in application, the course also intends to equip the students with a level of mathematical maturity needed for the more advanced courses in the Master of Financial Mathematics.

Course Learning Outcomes

Learning and Teaching Technologies

Moodle - Learning Management System | Zoom | Echo 360

Assessments

Assessment Structure

Assessment Details

Assignment 1

Assessment Overview

Working in groups, you will solve proof or calculation questions related to basic concepts in

probability theory and stochastic processes. You will have the chance to demonstrate your

understanding and mastery of the fundamental concepts and theory. You have three weeks to    complete this assignment, with the submission due in Week 4. Feedback will be provided within 2 weeks of submission.

Course Learning Outcomes

  CLO1 : State the most rudimentary concepts and theorems of measure-theoretic probability theory.

  CLO2 : Defne the properties of various stochastic process models and related random elements.

  CLO3 : Identify appropriate stochastic process model(s) for a given problem.   CLO4 : Provide logical and coherent proofs of important theoretic results.

Assessment Length

10 pages maximum

Submission notes

Typed up or neatly handwritten

Assignment submission Turnitin type

Not Applicable

Assignment 2

Assessment Overview

Working in groups, you will solve proof or calculation questions related to stochastic processes and their applications. In the process, you shall have the chance to demonstrate your

understanding and mastery of the theory and applications of relevant stochastic processes. You have three weeks to complete this assignment, with the submission due in Week 8. Feedback

will be provided within two weeks of submission.

Course Learning Outcomes

·  CLO1 : State the most rudimentary concepts and theorems of measure-theoretic probability theory.

  CLO2 : Defne the properties of various stochastic process models and related random elements.

  CLO3 : Identify appropriate stochastic process model(s) for a given problem. ·  CLO4 : Provide logical and coherent proofs of important theoretic results.

Assessment Length

10 pages maximum

Submission notes

Typed up or neatly handwritten

Assignment submission Turnitin type

Not Applicable

Assignment 3

Assessment Overview

Working individually, you will solve practical or theoretical questions related to stochastic

processes and their applications. In the process, you shall have the chance to demonstrate your  understanding and mastery of the theory and applications of relevant stochastic processes. You have three weeks to complete this assignment, with the submission due in Week 10. Feedback   will be provided within two weeks of submission.

Course Learning Outcomes

·  CLO1 : State the most rudimentary concepts and theorems of measure-theoretic probability theory.

·  CLO2 : Defne the properties of various stochastic process models and related random elements.

·  CLO3 : Identify appropriate stochastic process model(s) for a given problem. ·  CLO4 : Provide logical and coherent proofs of important theoretic results.

·  CLO5 : Apply the theory of stochastic processes to model real phenomena and answer some questions in applied sciences.

Assessment Length

6 pages maximum

Submission notes

Typed up or neatly handwritten

Assignment submission Turnitin type

Not Applicable

Final Examination

Assessment Overview

In the two hour exam, you will answer 4-5 questions related to the materials covered in this course. The difcultylevel of the questions will be comparable to those in your assignments and the sample example paper. The exam is held during the formal examination period, with feedback available through inquiry with the convenor.

Course Learning Outcomes

  CLO1 : State the most rudimentary concepts and theorems of measure-theoretic probability theory.

  CLO2 : Defne the properties of various stochastic process models and related random elements.

  CLO3 : Identify appropriate stochastic process model(s) for a given problem.   CLO4 : Provide logical and coherent proofs of important theoretic results.

  CLO5 : Apply the theory of stochastic processes to model real phenomena and answer some questions in applied sciences.

Assignment submission Turnitin type

Not Applicable

General Assessment Information

With the group assignments (Assignments 1 and 2), you must work in groups with around 5 members. You should collaborate in working out the answers to the assignment questions and make a single group submission by the due date. All members of a group should ensure you understand and approve of what is included in your group submission, and all members must sign their names on the cover of the submission, although only one member needs to click the 'submit'button (after all members agree to the submission). At the time of submission, all members of a group are required to do a short survey to evaluate and score group members' performance and contributions to the group work, and each member's assignment mark will be infuenced by the results of this peer evaluation process, so members in the same group might have different marks in the end.

With the individual assignment (Assignment 3), you can choose to work individually or in a group

(up to 5 members). If you choose to work in a group, you accept that your mark for this

assignment will be the same as your group members' (there will be no peer evaluation for this assignment).

Finally, please note that for assignments that are submitted after the due time, the standard late submission penalties apply.

Grading Basis

Standard

Requirements to pass course

Achieving a composite score of 50 out 100 at least

Course Schedule

Attendance Requirements

Students are strongly encouraged to attend all classes and review lecture recordings.

General Schedule Information

The following is a rough schedule we try to follow during the course.