## MA3AST-Applied Stochastic Processes

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:6
Terms in which taught: Autumn term module
Pre-requisites: MA2DE Differential Equations or MA2ODE Ordinary Differential Equations and MA2PDE Partial Differential Equations and ST1PS Probability and Statistics or ST1PD Probability and Distributions
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA3ASP Applied Stochastic Processes or MA4AST Applied Stochastic Processes
Module version for: 2017/8

Module Convenor: Dr Patrick Ilg

Summary module description:

This module introduces the concept of discrete and continuous stochastic processes, discusses their most important properties as well as a variety of applications from physics to finance.

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 be able to perform basic operations with them;

• to understand the concept of 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.

Outline content:

• Basic probability and probability distributions, change of variables, statistical independence, examples from game theory;

• 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 4 Guided independent study 76 Total hours by term 100.00 Total hours for module 100.00

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

Other information on summative assessment:

Two assignments and one examination paper.

Formative assessment methods:

Problem sheets.

Penalties for late submission:

Penalties for late submission on this module are in accordance with the University policy.
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.
• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the 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.

Length of examination:

2 hours.

Requirements for a pass:

A mark of 40% 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).

Additional Costs (specified where applicable):
1) Required text books:
2) Specialist equipment or materials:
3) Specialist clothing, footwear or headgear:
4) Printing and binding:
5) Computers and devices with a particular specification:
6) Travel, accommodation and subsistence:

Last updated: 31 March 2017