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 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
Current from: 2018/9
Module Convenor: Dr Patrick Ilg
Email: p.ilg@reading.ac.uk
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.
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.
Penalties for late submission:
Penalties for late submission on this module are in accordance with the University policy.
Assessment 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: 20 April 2018
THE INFORMATION CONTAINED IN THIS MODULE DESCRIPTION DOES NOT FORM ANY PART OF A STUDENT'S CONTRACT.