MA319-7-AU-CO:
Stochastic Processes
2016/17
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Postgraduate: Level 7
Current
15
05 March 2014
Requisites for this module
(none)
(none)
(none)
(none)
(none)
DIP GN1309 Mathematics and Finance,
MSC GN1312 Mathematics and Finance,
DIP G30009 Statistics,
MSC G30012 Statistics
The module introduces stochastic processes, principles of actuarial modelling and time series models and analysis.
On completion of the course students should be able to (learning outcomes):
- Understand concepts of stochastic processes;
- Understand properties of Markov chain models for discrete-state processes;
- Understand applications of Poisson processes;
- Understand basic concepts to model and to analyse time series
- Understand queue models and their properties.
Syllabus:
Stochastic processes
General stochastic process models. Random walks. Reflecting and absorbing barriers. Mean recurrence time, mean time to absorption. Difference equations. Branching processes. Markov chain models for discrete-state processes. Transition matrices: 1-step and n-step. Classification of states. Equilibrium distributions for time-homogeneous chains. Detail balance, general balance, limiting distribution, stationary distribution. Poisson processes. Differential-difference equations.
Birth and death processes.
Queues. The M/M/1 queue. Differential-difference equations. Conditions for equilibrium. Equilibrium distributions of queue size and waiting time for first-come-first-served queues. Extensions to M/M/k and M/M/ queues. The M/G/1 queue, imbedded Markov chain analysis. The Pollaczek-Khintchine formula. Mean queue length and waiting time.
Time series
Time series models; trend and seasonality. Stationarity. Autocovariance, autocorrelation and partial autocorrelation functions. Correlograms. Autoregressive (AR) processes. Moving average (MA) processes. ARMA processes. ARIMA processes and Box-Jenkins methods. Forecasting and minimising expected prediction
variance. Introduction to frequency domain analysis. Spectral density function. Periodograms.
No information available.
No information available.
No additional information available.
The module consists of 25 lectures, 5 classes. In the summer term 3 revision lectures are given.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Written Exam |
Test |
|
|
| Exam |
Main exam: 180 minutes during Summer (Main Period)
|
Additional coursework information
Information about coursework deadlines can be found in the "Coursework and Exams" section of the Current Students, Information for Students Maths web pages: Coursework and Test Information
Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Sypridon Vrontos, email svrontos@essex.ac.uk, tel 01206 874717
Mrs Shauna Meyers - Graduate Administrator. email: smcnally (Non essex users should add @essex.ac.uk to create the full email address), Tel 01206 872704
Yes
No
No
Prof John Nigel Scott Matthews
The University of Newcastle-upon-Tyne
Professor of Medical Statistics
Available via Moodle
Of 35 hours, 33 (94.3%) hours available to students:
2 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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