## MA4AST-Applied Stochastic Processes

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:7
Terms in which taught: Autumn term module
Pre-requisites: MA2DE Differential Equations and ST1PS Probability and Statistics
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA3AST Applied Stochastic Processes
Current from: 2021/2

Module Convenor: Dr Patrick Ilg

Type of module:

Summary module description:

To introduce the concept of stochastic processes and to enable students to solve problems involving stochastic processes from a variety of applications like molecular motion, population dynamics, weather and finances.

Aims:
To introduce the concept of stochastic processes and to enable students to solve problems involving stochastic processes from a variety of applications like molecular motion, population dynamics and finances.

Assessable learning outcomes:

By the end of the module students are expected to be able:

• to formulate and solve discrete stochastic processes using Markov chains;

• to solve diffusion-type partial differential equations for probability distributions;

• to understand stochastic integrals and stochastic differential equations and solve them in simple cases;

• to apply the above concepts to solve problems from a wide variety of fields from physics to finances;

• to familiarise yourself with a subarea of stochastic processes that are not covered in the lectures but are supported by additional material and a corresponding problem sheet.

This module will be assessed to a greater depth than the excluded module MA3AST.

Outline content:

• Discrete Markov chains, limit theorems, applications to population dynamics;

• Chapman-Kolmogorov equation, Markov processes, Wiener process, methods for solution of diffusion equation, examples from molecular motion and economics;

• Stochastic integrals, stochastic differential equations, their properties and methods of solution. Applications to Brownian motion and stock market.

Brief description of teaching and learning methods:
Lectures supported by problem sheets and tutorials.

Contact hours:
 Autumn Spring Summer Lectures 20 Tutorials 6 Guided independent study: 74 Total hours by term 0 0 Total hours for module 100

Summative Assessment Methods:
 Method Percentage Written exam 80 Set exercise 20

Summative assessment- Examinations:
2 hours.

Summative assessment- Coursework and in-class tests:

Two assignments and one examination paper.

Formative assessment methods:
Problem sheets.

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:
A mark of 50% overall.

Reassessment arrangements:
One examination paper of 2 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (80% exam, 20% coursework).