UNIVERSITY OF KENT
MODULE SPECIFICATION TEMPLATE
SECTION 1: MODULE SPECIFICATIONS
1.
Title of the module : Stochastic Processes (MA636)
2.
School or partner institution which will be responsible for management of the module
School of Mathematics, Statistics and Actuarial Science
3.
Start date of the module : Autumn 2005 (revised version start date September 2014)
4.
The number of students expected to take the module: approx.. 90
5.
Modules to be withdrawn on the introduction of this proposed module and consultation with other
relevant Schools and Faculties regarding the withdrawal
MA637
6.
The level of the module (e.g. Certificate [C], Intermediate [I], Honours [H] or Postgraduate [M]): H
7.
The number of credits and the ECTS value which the module represents : 15 (ECTS 7.5)
8.
Which term(s) the module is to be taught in (or other teaching pattern): Autumn term
9.
Prerequisite and co-requisite modules:
Prerequisite modules: Stage 1 modules: MA321 Calculus and Mathematical Modelling, MA322
Proofs and Numbers, and either MA323 Matrices and Probability and MA306 Statistics or MA319
Probability and Inference for Actuarial Science and MA326 Matrices and Computing; Stage 2
modules: MA552 Analysis, MA553 Linear Algebra and either MA629 Probability and Inference or
MA529 Probability and Statistics for Actuarial Science 2.
There are no co-requisite modules.
10. The programmes of study to which the module contributes
BSc (Hons) Actuarial Science, BSc (Hons) Financial Mathematics, BSc (Hons) Mathematics, BSc
(Hons) Mathematics & Statistics, BA (Hons) Mathematics and Accounting & Finance, (including
programmes with a year in industry), BSc (Hons) Mathematics with a Foundation Year, MMath
Mathematics, MMathStat Mathematics and Statistics
11. The intended subject specific learning outcomes
On successful completion of this module students will have:
a) a good understanding of the concepts involved in stochastic modelling;
b) a good knowledge of the various types of stochastic process (discrete or continuous time,
discrete or continuous state space);
c) a reasonable knowledge of the variety of techniques which can be used to obtain probabilities
and distributions arising in stochastic processes;
d) a reasonable ability to solve a variety of practical problems to which stochastic process
techniques can be applied.
12. The intended generic learning outcomes
Students who successfully complete this module will have:
1
UNIVERSITY OF KENT
a)
b)
c)
d)
further developed a logical, mathematical approach to solving problems;
enhanced their ability to work with relatively little guidance;
gained further organisational and study skills;
improved their key skills in written communication, numeracy and problem solving.
13. A synopsis of the curriculum



Principles. Principles and examples of stochastic modelling, types of stochastic process, types of
model, short-term and long-run properties
Markov chains. Relationships between generating functions for intervals between recurrences.
Applications. The Markov property. Markov chains. n–step transition matrix. Classification of
states. Equilibrium. Mean recurrence times. Time-inhomogeneous chains.
Markov processes. Examples of processes in continuous time. Poisson process. Birth and death
processes. Applications. Renewal processes. Queues and branching processes. Properties of
queues - arrivals, service time, length of the queue, waiting times, busy periods. The singleserver queue and its stationary behaviour. Queues with several servers. Classification of
queues.
14. Indicative Reading List
L. Breiman (1992), Probability, SIAM
L. Breuer and D. Banm (2005), A introduction to queuing theory and matrix-analytic methods,
Springer
E. Cinlar (1975), Introduction to stochastic processes, Prentice-Hall
S. Karlin and H.M.Taylor (1975), A first course in .stochastic processes, 2nd edition, Academic Press
T. Rolski et al (1999), Stochastic processes for insurance and finance, Wiley
S. Ross (1970), Applied probability models and optimisation applications, Dover
S. Ross (1983), Stochastic processes, John Wiley and Sons
15. Learning and Teaching Methods, including the nature and number of contact hours and the total
study hours which will be expected of students, and how these relate to achievement of the intended
module learning outcomes.
Number of contact hours: 36.
Number of independent learning hours: 114.
Total study hours: 150.
The theoretical material is presented mainly through lectures, which will contain appropriate worked
examples; these aim to illustrate all aspects of the theory underlying the curriculum for this module,
and to show how it is applied in practical cases (covering learning outcomes 11(a)-(d) and 12(a) and
(d)). Exercises challenge the students’ understanding of the technical material. They aim to reinforce
the theory and to demonstrate the range of applications of the topics covered in the module
(covering learning outcomes 11(a)-(d) and 12(a)-(d)). Notes on solutions to all exercises are supplied
to students. Some of the contact hours are devoted to discussion of the coursework.
16. Assessment methods and how these relate to testing achievement of the intended module learning
outcomes
The module will be assessed by examination (90%) and coursework (10%).
2
UNIVERSITY OF KENT
Examination: One 2–hour written exam in Summer term. The examination questions will require
descriptions of relevant techniques, together with solutions to theoretical problems and numerical
problems. The required answers will be of varying length, and will test learning outcomes 11(a)-(d)
and 12(a)-(d).
Coursework: Exercises will be given on individual components of the syllabus, and assignments will
be set involving selections from those exercises, to be completed outside contact hours. The
continuous assessment mark will be derived from marks on certain exercises. The exercises consist
of questions thatrequire mathematical manipulations and solution to numerical problems. Required
answers will vary in length. The exercises will test learning outcomes 11(a)-(d) and 12(a)-(d).
17. Implications for learning resources, including staff, library, IT and space
This is primarily a modification to the curriculum of an existing module and therefore there are no
special resource implications.
18. The School recognises and has embedded the expectations of current disability equality legislation,
and supports students with a declared disability or special educational need in its teaching. Within
this module we will make reasonable adjustments wherever necessary, including additional or
substitute materials, teaching modes or assessment methods for students who have declared and
discussed their learning support needs. Arrangements for students with declared disabilities will be
made on an individual basis, in consultation with the University’s disability/dyslexia support service,
and specialist support will be provided where needed.
19. Campus where module will be delivered: Canterbury
SECTION 2: MODULE IS PART OF A PROGRAMME OF STUDY IN A UNIVERSITY SCHOOL
Statement by the School Director of Learning and Teaching/School Director of Graduate Studies
(as appropriate): "I confirm I have been consulted on the above module proposal and have given advice
on the correct procedures and required content of module proposals"
................................................................
..............................................
Director of Learning and Teaching/Director of
Graduate Studies (delete as applicable)
Date
…………………………………………………
Print Name
Statement by the Head of School: "I confirm that the School has approved the introduction of the
module and, where the module is proposed by School staff, will be responsible for its resourcing"
.................................................................
..............................................
Head of School
Date
…………………………………………………….
Print Name
3
UNIVERSITY OF KENT
Module Specification Template
Last updated February 2013
4