Postgraduate Course: Stochastic Modelling (MATH11029)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Syllabus summary: Probability review: Conditional probability, basic definition of stochastic processes. Discrete-time Markov chains: Modelling of real life systems as Markov chains, transient behaviour, limiting behaviour and classification of states, first passage and recurrence times, absorption problems, ergodic theorems, Markov chains with costs and rewards, reversibility. Poisson processes: Exponential distribution, counting processes, alternative definitions of Poisson processes, splitting, superposition and uniform order statistics properties, non-homogeneous Poisson processes. Continuous-time Markov chains: transient behaviour, limiting behaviour and classification of states in continuous time, ergodicity, basic queueing models. |
| Course description |
Not entered
|
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Probability (MATH08066)
|
Co-requisites | |
| Prohibited Combinations | Students MUST NOT also be taking
Stochastic Modelling (MATH10007)
|
Other requirements | Open only to School of Mathematics MSc programmes.
Note that PGT students on School of Mathematics MSc programmes are not required to have taken pre-requisite courses, but they are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling. |
Course Delivery Information
|
| Academic year 2024/25, Not available to visiting students (SS1)
|
Quota: None |
| Course Start |
Semester 1 |
| Course Start Date |
16/09/2024 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 20,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
66 )
|
| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S1 (December) | Stochastic Modelling (MATH11029) Postgraduate | 2:120 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Formulate mathematically a range of real-life scenario of a stochastic process described in words.
- Demonstrate an understanding of discrete and continuous time stochastic processes by being able to calculate finite dimensional distributions.
- Analyse the transient behaviour of Markov chains, and classify their states.
- Demonstrate an understanding of stationary and limiting behaviour by deriving corresponding probability distributions, and first passage properties.
- Calculate the finite dimensional distributions of Poisson processes.
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Reading List
| R. Durrett. Essentials of Stochastic Processes, Springer, 2012. V. Kulkarni. Modeling and Analysis of Stochastic Systems, CRC Press, 2010. |
Contacts
| Course organiser | Dr Theo Assiotis
Tel:
Email: theo.assiotis@ed.ac.uk |
Course secretary | Miss Gemma Aitchison
Tel: (0131 6)50 9268
Email: Gemma.Aitchison@ed.ac.uk |
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