# STOCHASTIC PROCESSES - 2022/3

Module code: MAT2003

Module Overview

Realistic modelling often requires the inclusion of stochastic (as opposed to deterministic) elements. In this module we study a large class of stochastic processes, that is, probabilistic models for series of events.

Module provider

Mathematics

KUEH Audrey (Maths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 5

JACs code: G330

Module cap (Maximum number of students): N/A

Independent Learning Hours: 106

Seminar Hours: 11

Module Availability

Semester 1

Prerequisites / Co-requisites

None

Module content

Indicative content includes:

• concept of stochastic process;

• random walks;

• properties of Markov chains: recurrence and transience, periodicity, communicating classes, irreducibility;

• first step analysis;

• Basic Limit Theorem, stationary distributions, and their applications;

• Markov processes in continuous time: derivation of the Poisson process and generalised birth and death process.

Assessment pattern

Assessment type Unit of assessment Weighting
Online Scheduled Summative Class Test ONLINE TEST 20
Examination Online ONLINE EXAM 80

Alternative Assessment

N/A

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate

·         Understanding of and ability to interpret and manipulate mathematical statements.

·         Subject knowledge through the recall of key definitions, theorems and their proofs.

·         Analytical ability through the solution of unseen problems in the in-semester test and in the exam.

Thus, the summative assessment for this module consists of:

·         One two hour examination; worth 80% of the module mark.

·         One in-semester test; worth 20% of the module mark.

Formative assessment and feedback

Students receive written feedback via marked unassessed coursework.  In addition, verbal feedback is provided by lecturer/class tutor at biweekly tutorial lectures.

Module aims

• This module aims to introduce students to stochastic processes and their applications.

Learning outcomes

Attributes Developed
1 Understand the properties of stochastic processes  KCP
2  apply this knowledge to analyse specific stochastic processes, occurring for example in finance or biology. KCPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to introduce students to the theory of stochastic processes.

The learning and teaching methods include:

• 3  hour lectures per week x 11 weeks, on the blackboard  and Q + A opportunities for students;

• Including (every second week) a tutorial lecture for guided discussion of solutions to problem sheets or unassessed coursework provided to and worked on by students in advance.

• Including revision lectures (in week 12).

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.