MATH3361: Stochastic Differential Equations

- 2 x class tests (7.5% each, totalling 15%)
- Lab test (15%)
- Assignment (20%)
- Final exam (50%).

The official pre-requisite is MATH2011 or MATH2111 or MATH2018 (DN) or MATH2019 (DN) or MATH2069 (DN) and MATH2801 or MATH2901 or MATH2089 (DN) or MATH2099 (DN).

This course made me appreciate the things we took for granted in MATH2901. The course begins with some discussions on stochastic analysis (which is probably the most pure component of the course) before the discussion on stochastic differential equations begin. If you're a stats major looking for an elective, this course is definitely something to consider. For the bulk of the course, however, it places a heavy emphasis on the differential equations aspect, as well as some discussions on some numerical approximations using Euler-Maruyama and Milstein.

- 1 x 2 hour live lecture.
- 1 x 1 hour tutorial.
- 1 x 1 hour lab.

3/5

Yes.

- Lecturer: Prof. Thanh Tran

Lecture slides are sufficient.

4.5/5

None prescribed.

2021 Term 1

88 (HD).

- 15% written test, split into two parts (I think each part was basically 7.5%)
- 15% lab test
- 20% assignment
- 50% final exam

Specified for 3361 are one of:
- MATH2011, MATH2111, MATH2018 (DN), MATH2019(DN), MATH2069(DN). and
- MATH2801, MATH2901, MATH2089(DN), MATH2099(DN)
No formal prerequisite specified for 5361, but should be about the same as the above.

This course is one of several level 3 applied mathematics courses offered. Stochastic DEs address one key drawback from ordinary DEs, that everything has to be deterministic. Take something simple like modelling stocks, and inevitably there will be what looks like randomness in the stock price. Another could be just basic population growth, which we can't assume in general must be deterministic like exponential growth.

Admittedly, this course felt extremely comfortably relaxing prior to the finals. It felt like another where although the lectures were full on, the assessments were much friendlier and not demanding at all to do, provided you carefully studied everything. There's only 2 hours of lecture a week, so there's also less content to be absorbed.

Coding is done in MATLAB, and was assessed in the lab test and assignment. Generally speaking, it suffices to carefully study all the labs (but in particular, the numerical methods). MATLAB documentation was allowed for these, from memory. For the most part, Thanh cares about your code doing the right thing. (Missing a minor code optimisation was probably allowed.)

It also helped a lot that for minor errors, Thanh would point them out, yet not penalise. Helps understanding, and isn't harsh on the marks either.

You should definitely have some minor stats background before coming into this course (MATH2801/2901 is definitely enough). It is stochastic differential equations after all. MATH2121/2221 experience is not required (ordinary differential equations) at all, but if you took it then you might understand the Karhunen-Loeve expansion a little more quickly than others.

The difficulty pretty much all came from the final exam. Which had some relaxing questions early on, but gradually stemmed into what felt like a watered down analysis paper. Certainly felt harder this year than in other years to do, and was a little stressful. I later verified that 5361 had a couple extra questions on top of 3361. (Which was unfortunate, because I did struggle more in the 5361 only questions.)

Knowing how to use inequalities was helpful for this year's exam in particular. The inequalities were provided for you in the exam (i.e. less memorisation), but it was often hard puzzling where to use it. (Whereas for the past paper, it felt more like an ability to manipulate limits and sums.) These are all pretty common tools for proofs in analysis though. Not sure how many students would've fought through all of it.

An observation is that numerical methods seemed to appear more in the coding component, whilst everything else (elementary stochastic analysis, stochastic integrals, stochastic DEs) seemed to appear more in the theory. But still, numerical methods was also in the theory. KL expansions and GFE methods destroyed my head way more than pre-cursor topics, but that was not surprising. It does also mean that you should pay closer attention to those topics, for the finals.

2hr lecture, 1hr laboratory, 1hr tutorial

4/5 (mostly due to finals; up until then it's really just 2/5 at most)

Yes, as per usual in COVID times. Also tutorial recordings.

Prof. Thanh Tran

Lectures, tutorials, and lab exercises gradually uploaded. Pretty standard for maths courses. Some introductory MATLAB notes are also provided.

4.5/5

No prescribed as far as I could tell. Reference books can be found in the course outline.

21 T1

96 HD