- Student Records
Programme & Unit Catalogues


MA30125: Markov processes & applications

[Page last updated: 15 October 2020]

Follow this link for further information on academic years Academic Year: 2020/1
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Honours (FHEQ level 6)
Further information on teaching periods Period:
Semester 1
Further information on unit assessment Assessment Summary: EX 100%
Further information on unit assessment Assessment Detail:
  • Examination (EX 100%)
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA20225
Description: Aims:
To study a variety of Markov processes in both discrete and continuous time, including simple Lévy processes. To give a basic introduction to martingales and demonstrate their use. To apply results in areas such as genetics, biological processes, queues, telecommunication networks, insurance, electrical networks, resource management, random walks and elsewhere.

Learning Outcomes:
On completing the course, students should be able to:
* Formulate appropriate Markovian models for a variety of real world problems and apply suitable theoretical results to obtain solutions;
* Classify a birth-death process as explosive or non-explosive;
* Find the Q-matrix of a time-reversed chain and make effective use of time reversal to describe departures from queues;
* Compute basic properties of branching processes;
* Perform standard computations for simple Lévy processes;
* Verify the martingale property and use martingales effectively in applications.

Skills:
Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials)

Content:
Topics covering discrete and continuous time Markov chains, simple Lévy processes and some applications of martingales will be chosen from:
Resource management: warehouse restocking, reservoir model. Telecommunication models: blocking probabilities for land line and mobile networks. Queuing networks: M/M/s queue, departure process. Series of M/M/s queues. M/G/1 queue. Reflecting random walks as queuing models in one or more dimensions. Open and closed migration networks. Simple genetics models: Wright-Fisher and Moran models. Kingman's coalescent process. Population models and branching processes: Birth-death processes. Continuous time Galton-Watson processes. Extinction probabilities. Population growth. Epidemics. Markov processes: Stopping times. Strong Markov property. Explosions. Ergodic theorem. Stationarity. Time reversal. Reversibility. Basic martingales and applications: statement of convergence theorem, discussion of optional stopping theorem. Change of measure. Simple Lévy processes: Compound Poisson Processes with drift. Stationary independent increments. Characteristic exponents. First passage problems. Applications to continuous time workload model and ruin problems in insurance. Markov random fields. Electrical networks. Other applications.
Further information on programme availabilityProgramme availability:

MA30125 is Optional on the following programmes:

Department of Economics
  • UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 3)
  • UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 4)
  • UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 4)
  • UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 4)
Department of Mathematical Sciences
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
  • USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
  • USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
  • USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
  • USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
  • USMA-AFB05 : BSc(Hons) Statistics (Year 3)
  • USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
  • USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

Notes: