# 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 & Physics

### Module Leader

KUEH Audrey (Maths & Phys)

## Overall student workload

Independent Learning Hours: 102

Lecture Hours: 28

Tutorial Hours: 11

Captured Content: 9

Semester 1

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
School-timetabled exam/test In-semester test (50 minutes) 20
Examination Exam (2 hours) 80

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 lectures and seminars.

## 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:

• lectures on the blackboard and Q + A opportunities for students;

• tutorials for guided discussion of solutions to problem sheets or unassessed coursework provided to and worked on by students in advance;

• revision lectures.

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.

## Reading list

https://readinglists.surrey.ac.uk
Upon accessing the reading list, please search for the module using the module code: MAT2003

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2022/3 academic year.