Random processes (L.7) (862G1)
Random processes (L.7)
Module 862G1
Module details for 2023/24.
15 credits
FHEQ Level 7 (Masters)
Pre-Requisite
Pre-requisite: Level 6: (G1100) Probability Models [T1]
Module Outline
Rationalisation:
After the introduction of the Poisson process, birth and death processes as well as epidemics models can be presented in full generality as applications of the pooled Poisson process. At the same time, the students will be introduced to the Kolmogorov equations and to the techniques for solving them. Renewal theory is needed to better understand queues, and, for this reason, it is discussed before queues.
Modernisation:
A modern introductory course on stochastic processes must include at least a section on compound renewal processes (with a focus on the compound Poisson process) as well as a chapter on the Wiener process and on Ito stochastic calculus. This is necessary given the importance this process has in several applications from finance to physics. Modernisation is achieved by including a new introductory chapter divided into three parts.
1. Poisson processes:
a. Density and distribution of inter-event time.
b. Pooled Poisson process.
c. Breaking down a Poisson process.
d. Applications of the Poisson process, e.g. birth-and-death processes, the Kolmogorov equations.
2. Renewal processes:
a. The ordinary renewal process.
b. The equilibrium renewal process.
c. The compound renewal process.
d. Applications of renewal processes, queues.
3. Wiener process:
a. Definition and properties
b. Introduction to stochastic integrals
c. Introduction to stochastic differential equations.
Module learning outcomes
Systematic understanding of the assumptions underlying continuous time models and how the models are derived.
Develop advanced skills to be able to analyse the models mathematically and to isolate the important factors.
Know how to relate continuous time processes to discrete analogues and embedded processes.
Comprehensive understanding of the Markov property and developing the ability to identify when it applies, and be able to analyse the models and apply them to different examples.
| Type | Timing | Weighting |
|---|---|---|
| Unseen Examination | Semester 2 Assessment | 80.00% |
| Coursework | 20.00% | |
| Coursework components. Weighted as shown below. | ||
| Problem Set | T2 Week 8 | 15.00% |
| Problem Set | T2 Week 10 | 15.00% |
| Problem Set | T2 Week 5 | 15.00% |
| Problem Set | T2 Week 3 | 15.00% |
| Portfolio | T2 Week 11 | 40.00% |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Spring Semester | Lecture | 2 hours | 11111111111 |
| Spring Semester | Lecture | 1 hour | 11111111111 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.
Dr Antoine Dahlqvist
Convenor, Assess convenor
/profiles/472549
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