## 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

Type of module:

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

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:

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).